Nathan Broadhead scored the opener for Everton
Nathan Broadhead put the Blues ahead in the first half when he headed Luke Garbutt's left-wing cross home with 18 minutes left.
Theo Widdrington had Pompey's U23s level shortly afterwards from the penalty spot but when Antony Evans nodded another Garbutt cross back to Lavery, he rifled home to make it 2-1.
Everton U23s: Gray; Denny, Ouzounidis, Foulds; Markelo, Baningime (74' Evans), Baxter (c) (56' Lavery), Garbutt; Broadhead, Donkor (65' Byrne), Sambou.
Subs not used: Hilton, Henen.