Austria international Arnautovic marked his 100th game for Stoke with his ninth and 10th goals of the season in the space of five minutes in the second half at the Britannia Stadium.
Leandro Bacuna got one back for Villa late on, but the defeat was another crushing blow for the woeful visitors, who are eight points from safety with only 11 games remaining to salvage their top-flight status.
Villa manager Remi Garde has won just three of his 19 games since replacing the sacked Tim Sherwood in November and his troubled club look destined to drop into the second tier for the first time since 1988.
Their 17th league defeat in 27 matches this season was a familiar tale, with defensive deficiencies and attacking ineptitude proving a fatal combination once again.
Rocked by a 6-0 thrashing against Liverpool in their previous match, Garde had reacted to Villa's worst home defeat in 81 years by publicly questioning the commitment of his players.
The former Lyon coach hardly got the response he was looking for when a side comprised of Villa's youth academy prospects defeated his first team 3-0 in a practice match last week.
Yet Garde still made only one change from the Liverpool humiliation as captain Micah Richards was replaced by Alan Hutton, meaning Joleon Lescott kept his place despite his recent Twitter row with angry Villa fans.
Villa had conceded a deluge of early goals against Liverpool and they almost made another bad start when Jores Okore turned a Stoke cross towards his own net, with goalkeeper Mark Bunn scrambling back to keep it out.
Stoke, buoyed by a win over Bournemouth that ended a run of three successive 3-0 league defeats, were in complete control and Xherdan Shaqiri curled a free-kick wide before Geoff Cameron headed over.
If Villa, without an away win since August, took encouragement from making it to the interval on level terms, they were swiftly plunged back into despondency six minutes after halftime.
Ashley Westwood summed up Villa's habit of shooting themselves in the foot when he conceded a needless penalty with a crude barge into Phil Bardsley and Arnautovic stepped up to send Bunn the wrong way from the spot.
Mark Hughes' men scented blood now and Arnautovic was the executioner in the 56th minute.
Arnautovic headed Shaqiri's cross straight up in the air but, with Villa's leaden-footed defenders failing to react, the Austrian had time to recover and chest the ball home after Bunn embarrassingly stumbled into the net.
Villa were given a lifeline when Bacuna fired home in the 79th minute, but it was too late to spark an unlikely fight back.