Aston Villa's Wesley in action with Everton's Morgan Schneiderlin and Dominic Calvert-Lewin on Friday. Reuters
After losing to Tottenham and Bournemouth in their first two games, Villa finally got their campaign up and running on their return to the top flight after a three-year absence.
Dean Smith's promoted side were already being written off as relegation fodder following their nervous start to the season.
But Wesley's first goal since the forward's £22 million ($27 million) close-season move from Belgian side Club Brugge lifted the mood at Villa Park in the 22nd minute.
Anwar El Ghazi added the second in stoppage-time to ensure Villa were able to celebrate the end of a 15-match winless run in the Premier League dating back to a victory over Norwich in February 2016.
"It was very sweet. It was a hard-earned win. We always looked a threat on the break. To get that goal at the end just capped it off," Smith said.
"Our defensive organisation was good. I always thought we would score a second, but I thought it would come a bit earlier.
"Getting your home results in this league is a important and getting your first one is massive."
Everton paid the price for poor finishing as they wasted chances to maintain their unbeaten run, which came to an abrupt end after a draw against Crystal Palace and a victory over Watford.
"It is really difficult to see how we can lose this game when we create so many chances to score," Everton boss Marco Silva said.
"It is concerning about the goals we didn't score and of course we should score more. Against Palace we created lots of chances to score and didn't and again today."
Jack Grealish had lost a record 20 successive Premier League games with Villa — dating back to their previous spell in the top flight — and he was fortunate not to concede an early penalty for a challenge on Richarlison.
Grealish set about ending his dismal losing streak when he cleverly took a quick free-kick inside his own half that caught Everton flat-footed.
Grealish picked out Jota and he advanced down the left flank before slipping a superb pass to Wesley, who found the bottom corner with a fine finish.
Wesley threatened a second goal moments later but this time his shot was blocked by Yerry Mina's sliding challenge.
Everton should have equalised when Morgan Schneiderlin found Seamus Coleman and he clipped a pass to Dominic Calvert-Lewin, whose first-time shot was blocked on the line by Villa defender Bjorn Engels.
Everton hadn't come from behind at half-time to win a Premier League game since September 2015 and that run was destined to continue.
Silva tried to spark his team by sending on former Arsenal winger Alex Iwobi for his debut along with ex-Juventus striker Moise Kean.
Iwobi had an immediate impact and he turned to fire against the post in the closing moments.
Theo Walcott should have equalised in the 90th minute but the unmarked substitute somehow fired over from close range as he took a hurried swipe at Kean's cross.
And El Ghazi wrapped up the long-awaited points for Villa when he slotted home John McGinn's pass from six yards in the fifth minute of added time.
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