Villa struck early after Marc Guehi lost possession inside his own penalty area. The defender was punished as Jackson created space before firing into the roof of the net to give the hosts the lead.
Manchester City responded with pressure, but Villa goalkeeper Zion Suzuki produced an excellent save to deny Iliman Ndiaye's curling effort. Suzuki then kept out a low shot from Rayan Cherki, while Ndiaye struck the post as City searched for an equaliser before half-time.
City found their breakthrough 10 minutes after the restart. A cleverly worked free-kick created the opportunity for Ndiaye to deliver a cross towards the far post, where Erling Haaland rose to head home and bring the visitors level.
The momentum appeared to be with City when Suzuki tipped Josko Gvardiol's powerful strike onto the crossbar. However, Villa quickly turned defence into attack, and Jackson restored their advantage with a low shot that slipped beneath goalkeeper Gianluigi Donnarumma.
Suzuki continued to frustrate City, reacting sharply to prevent Gvardiol from converting a loose ball inside the penalty area. Villa were forced to defend deep during the closing stages, but Unai Emery's side remained organised under sustained pressure.
City came close to rescuing a point when Haaland's late header looked destined for the net, only for Ian Maatsen to clear the ball off the line.
Villa held on for a valuable victory, while City missed the opportunity to become only the eighth team in English top-flight history to win their opening eight league matches of a season.
Nigerian international Alex Iwobi's versatility and quality have earned high praise from Coventry City manager Frank Lampard, who believes the Fulham midfielder was already a good player before their time together at Everton.
Bradley Barcola is available for Liverpool's Premier League meeting with Brighton at Anfield on Sunday, but Dominik Szoboszlai has been ruled out as the Reds continue a demanding run of fixtures.
Arsenal manager Mikel Arteta could hand Max Dowman an increased role in the first team after Bukayo Saka was ruled out for up to eight weeks with a quad injury.
Manchester United head coach Michael Carrick will be looking for an immediate response when his side host Bournemouth at Old Trafford, after their humiliating Champions League defeat to Como.
