Everton are through to the semi-finals of the League Cup for the first time in eight years thanks to a professional display at the Riverside that was lit up by two wonderful goals, scored by Gerard Deulofeu and Romelu Lukaku.
The Spaniard whipped home a tremendous solo effort in the 20th minute to press home the Blues' early dominance and then served up a vital second goal eight minutes later for Lukaku to head home.
The annoyance at the passing up of two vital points against Bournemouth will no doubt resurface as Monday's Premier League fixture against Crystal Palace approaches but it's been replaced and certainly diminished in the interim by the glow of this victory and the fact that Everton's quest to end what will be a 21-year trophy drought by the time the finals of the two domestic cup competitions roll around took another step closer to glory.
The manager and supporters alike 5,600 of whom travelled to the Riverside Stadium to raucously spur the Toffees on to the next round demanded that the players learn from their mistakes on Saturday and Everton were handed an immediate opportunity to prove they had learned the harsh lesson as they charged into another 2-0 half-time lead.
This time they used the luxury of that two-goal advantage more wisely; the entertainment might not have been there in the second period indeed, Everton lapsed into occasional sloppiness at times but Martinez's players executed an effective strategy of largely controlling the ball and frustrating an opponent that was well-organised and game enough but which couldn't find the quality to reguarly break the visitors down.
Having made a raft of changes to his team in previous rounds, Martinez demonstrated how seriously he is now taking the Capital One Cup by making just two unenforced altterations to the side that had started each of the last two league games. James McCarthy was ruled out with a hip injury and was replaced by Tom Cleverley, Joel Robles deputised as expected for Tim Howard while Leon Osman was named captain and deployed in attacking midfield behind Lukaku, with Ross Barkley dropping into a more withdrawn role.
While the stand-in skipper often looked off the pace and light-weight, it was a formation that ultimately worked as the Blues' overall dominance and superior quality told after 20 minutes. They had started in composed fashion, happy to keep the ball and probe for openings, and an early chance for Seamus Coleman to cross came from a lovely pass by Deulofeu which eventually resulted in back-to-back corners that came to nothing.
A strong run by Lukaku in the 11th minute ended with an inviting square ball across the Boro box that wasn't anticipated by a Blue jersey but when the Blues got it back, Deulofeu's cross just eluded the Belgian's head in the middle.
Having been subdued by the visitors for the opening quarter of an hour, Middlesbrough began to grow in the contest and after Funes Mori had fouled Cristhian Stuani, Robles had to help Stewart Downing's free kick behind with a one-handed save. Stuani had the ball in the net from the resulting corner but he had clearly fouled the goalkeeper in the process.
The first goal was all down to Deulofeu who picked the ball up near the centre circle, surged down the middle towards Middlesbrough's area, cut inside Ben Gibson leaving the defender on his backside and then paused to size up his options before whipping a shot into the corner of the goal from 20 yards.
Everton's second was a glorious illustration of the talented attacking team that Martinez has built as more magic by Deulofeu served up a sixth goal in five games for Lukaku. Ross Barkley swept a cross-field delivery to the Spaniard for the penultimate ball in a 28-pass move that Deulofeu chested down, mesmerised Fernando Amorebieta with a number of step-overs before delivering in across from the byline that Lukaku guided smartly into the far corner from the near corner of the six-yard box.
Boro responded with what they could muster, forcing Robles to save low from Stuani's low cross-cum-shot while Kike lifted a shot dangerously close to the far post following an error by Funes Mori and Downing whistled another free kick narrowly wide. Lukaku and Barkley, meanwhile, spurned a threatening counter-attack with a poor final ball from the Belgian that might otherwise have put the England international in for a shot on goal.
Not surprisingly, Everton emerged from the half-time interval in less urgent mood and much of the first quarter of an hour in the second period was about Boro trying to probe their way through the Blues's back line. The travelling fans had their hearts in their mouths a couple of times as Deulofeu went down under Fernando Amorebieta's late tackle and John Stones stayed down following an equally heavy tackle but both players recovered to play on.
Robles, meanwhile, had to be at his best to push Downing's rasping drive over the bar a couple of minutes shy of the hour mark and the home fans were baying for a penalty a few minutes for handball on Funes Mori but referee Roger East wasn't interested a sit appeared to strike his shoulder. Stuani, unmarked, then despatched what would prove to be the home team's best chance over the bar from a right-wing cross.
With the visitors looking flat and a little leggy, changes were needed from Martinez as the game entered the final 20 minutes but it was Leighton Baines's long-awaited return to action that heralded the first substitution. He replaced Galloway in the 72nd minute and was booked almost immediately for protesting a little too vehemently at the referee's refusal to stop the game after Deulofeu was caught by an arm across the face.
Kevin Mirallas was then handed a chance to stake a claim for more playing time when he replaced Deulofeu for the last 10 minutes and he almost marked the occasion with a goal but his side-foot shot was blocked by Mejias and the most notable part of his cameo was how quickly he disappeared down the tunnel after the final whistle while his teammates applauded the massed ranks of jubiant Evertonians in the away end.
The Toffees now await tomorrow's semi-final draw in anticipation knowing that triumph over to legs in the next round would see them through to a first Wembley final since 2009. As an attacking unit, with 16 goals scored in their last five games, Everton are as exciting a team as any in the top flight at the moment and should, on this evidence, fear few opponents but it's at the back where the key to their fate may lie. If they can firm up in defence Baines's return can only help in that regard then cup glory is certainly within their grasp.
Everton step back on the road to Wembley this evening with a trip to the northeast to face Middlesbrough in the quarter finals of the Capital One Cup that they hope will swiftly diminish the disappointment of their last Premier League outing.
It's a cup tie that was already pregnant with expectation and anticipation for Evertonians but one which has taken on extra significance in the wake of Saturday's gut-wrenching 3-3 draw against Bournemouth. For supporters sensing the glimmers of opportunity in a season where the top four feels wide open, the Blues' spurning of two vital points came as another reality check and, perhaps, returned the League Cup to the forefront of the team's hopes of answering Roberto Martinez's increasingly oft-repeated refrain that Everton "have to achieve" this season.
This competition may have been unkind to the Blues since its inception five-and-a-half decades ago but, sitting as they are just three games away from a first Wembley final in seven years, it represents the next and, for now, the most likely means of the club ending the longest trophy drought in its history.
Martinez has already suggested that his players will respond in the right way following their late lapse at the Vitality Stadium but all Blue eyes will be on which personnel the manager selects for what is arguably the most important match that Everton have faced since the Europa League round of 16 second leg in Kiev last March.
The Catalan has already shown a propensity to make a raft of changes in the earlier rounds of the Capital One Cup this season on each occasion they needed to come from behind to rescue the tie and they survived the lottery of a penalty shootout in the last round to overcome Norwich and more shuffling of the deck is expected against Boro. although the hope is that they won't be too extensive or disruptive.
Martinez has already confirmed that Joel Robles will start the game, just as he did in the previous three rounds, but at least one further alteration to the team that started against Bournemouth could be forced on the manager after James McCarthy came off with a hip on Saturday. Termed by his boss as "an over-extension", it's unlikely to keep him out for long but it makes him doubtful for this tie in any case, it would surely be prudent to keep him out as a precaution even if it likely means no rest for Gareth Barry.
Tom Cleverley was McCarthy's replacement at Dean Court at the weekend and could deputise in the defensive midfield role, but Muhamed Besic will also be champing at the bit after his protracted lay-off with a hamstring problem and Darron Gibson is another candidate to fill the void. All three could end up playing, however, if Barry hasn't recovered from a shin injury that he sustained on Saturday and the manager decides to deploy Cleverley on the left where Kone operated last time out.
Further forward, Kevin Mirallas and Aaron Lennon will be similarly eager for playing time and both could start if Martinez elects to rest Arouna Kone and Gerard Deulofeu after their exertions on Saturday both players looked tired in the final quarter of an hour against the Cherries.
Finally, much attention will be focused on the left back slot when the teams are announced before kick-off to see if Leighton Baines's name is in the line-up. The 30-year-old hasn't been risked in either of the last two games despite being declared "medically fit" by Martinez a fortnight ago. The manager has wisely been playing it safe with the England international and it wouldn't be surprising to see him sit this one out as well, perhaps with next Monday's important game against Crystal Palace in mind.
Given how well Everton have been performing away from home this season they have lost just once away from Goodison Park so far and that they beat Reading from the same division as Middlesbrough in the League Cup earlier in the campaign, the team should travel in good spirits and with the knowledge that if they perform to their ability and defend better than was the case against Bournemouth then they should be able to see this one out.
Of course, it is a cup tie and Boro, whose manager Aitor Karanka has a full squad from which to choose, will be just as up for it. Everton, though, will be backed by a passionate and vocal travelling army that will, no doubt, be seeking to revisit the atmosphere of another trip to this part of the world in 2012 when the Blues produced an irresistable display to beat Sunderland and book their place in the FA Cup semis of that year.
A repeat of that performance at the Stadium of Light and a chance at redemption for what followed at Wembley against Liverpool would do nicely.