Wesley Moraes, who arrived from Club Brugge for a club record fee in the summer, opened his account in English football with a close-range effort from Jota's incisive pass in the 21st minute at Villa Park.
Villa did get threatened late on as Alex Iwobi struck the post with eight minutes remaining and Theo Walcott spurned a great opportunity.
However, the hosts managed to make sure of victory when substitute Anwar El Ghazi's shot crept under the body of Jordan Pickford deep into injury time.
The result lifted Dean Smith's side up to 11th in the fledgling Premier League table, with Everton's first defeat of the season put them ninth ahead of the remaining fixtures this weekend.
Lineker, who had a prolific season at Goodison Park in 1985-86 before moving to Barcelona, believes that Villa finally getting off the mark will be a huge psychological boost for them going forward.
Huge victory for @AVFCOfficial. So important psychologically to get those first 3 points. Well played.— Gary Lineker (@GaryLineker) 23 August 2019
Indeed, considering the team's prior losing run in the top flight, which began back in 2015-16 and stretched into the first two games of this season, it certainly is a big weight off the shoulders of the team, particularly for captain Jack Grealish.
Up next for Aston Villa is their Carabao Cup trip to Crewe Alexandra on Tuesday night before heading to Selhurst Park at the weekend to lock horns with Crystal Palace.
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