Evans scored the winner with 17 minutes to go after Bassala Sambou had hit the woodwork with a penalty earlier in the half.
Funes Mori played 74 minutes alongside Mason Holgate as his comeback from a serious knee injury continues.
The win puts the Blues' U23 team into the knockout phase of the Premier League Cup.
Everton U23s: Hewelt, Markelo, Gibson, Denny, Holgate (60' Feeney), Funes Mori (74' Collins), Evans, Grant (62' Baxter), Hornby, Sambou, Henen. Subs not Used: Hilton, Lavery.