Wesley opened his Premier League account with a smart first-half finish at Villa Park on Friday, the first goal Everton has conceded this season after keeping clean sheets in its opening two matches.
Marco Silva threw on new signings Moise Kean and Alex Iwobi, the latter making his debut after joining from Arsenal, but the Toffees could not find an equaliser and Anwar El Ghazi added a late second on the break.
Everton started on top and Richarlison saw a penalty appeal rejected but Villa struck the opener soon after in the 21st minute.
Jack Grealish took a quick free-kick and Jota's superb pass caught Michael Keane sleeping, with Wesley bursting clear to finish well past Jordan Pickford.
Yerry Mina's block denied Wesley a rapid second and Dominic Calvert-Lewin wasted a clear opening at the other end before half-time.
Substitute Iwobi went closest to equalising for the visitors with nine minutes to go, but his instinctive strike came back off the post with Tom Heaton beaten, then Theo Walcott missed another good chance.
Dean Smith's men punished those errors with a second strike on the break, play-off final hero El Ghazi slotting in to get Villa up and running after they lost their first two games against Tottenham and Bournemouth.