Jhon Duran finished off a fine team move to give the home side an early lead and Morgan Rogers doubled Villa's advantage in the 65th minute.
Phil Foden scored his first Premier League goal of the season in stoppage time but it proved to be too little too late.
Pep Guardiola, in the worst run of his glittering career, said Friday that "sooner or later" things will turn around but City's fear factor has vanished.
The win lifts Unai Emery's inconsistent Villa team to fifth in the Premier League table, one place above sinking City.
Guardiola made six changes to the team side that lost last week's Manchester derby, bringing in goalkeeper Stefan Ortega and reshaping his defence with Rico Lewis, John Stones and Manuel Akanji.
Mateo Kovacic and Jack Grealish also returned.
But the defending champions started the match in chaotic fashion and could have been behind inside 20 seconds.
Untidy work from Josko Gvardiol allowed John McGinn to steal the ball and he fed Duran, whose shot from outside the box was pushed behind by Ortega.
Villa were millimetres away from taking the lead from the resulting corner, with Ortega, in for first-choice goalkeeper Ederson, producing a superb save to deny Pau Torres.
City then settled and their possession numbers topped 75 percent but they created little.
Instead it was Villa who took the lead through Duran after a superb team move, scoring his seventh Premier League goal of the season.
Youri Tielemans delivered a wonderful defence-splitting pass to Rogers, who burst through City's backline with ease before finding Duran on his right and the Colombian international finished crisply.
Phil Foden tested Villa goalkeeper Emiliano Martinez in the 35th minute after an incisive move involving Lewis.
And Gvardiol squandered a glorious chance moments before half-time, heading over a Grealish cross.
Guardiola brought on Kyle Walker for Stones at the break.
Minutes into the second half Villa's Matty Cash lashed an attempt into the side netting after a speedy attack before Duran had a strike ruled out for offside.
Rogers hit the foot of the post just before the hour mark after an intricate team move down the left.
Emery's men doubled their lead 20 minutes into the second half, with Rogers finishing unerringly from a McGinn pass.
City created little as they searched for a way back into the game until Foden pounced for a late consolation goal.
