The 31-year-old striker, on loan from Los Angeles Galaxy, drew the visitors level in the 51st minute and then claimed a late winner to give Villa coach Alex McLeish something to smile about on his 53rd birthday.
Darren Bent had put Villa in front with an 11th-minute penalty, before Wolves turned the game around through goals from Michael Kightly and David Edwards.
Villa's third away win of the season lifted them from 13th to 11th in the Premier League table, while Wolves slipped into the relegation zone after their eighth consecutive league game without a win.
It marked a miserable end to the week for Mick McCarthy's side, who were eliminated from the FA Cup in mid-week by Midlands rivals Birmingham City.
Wolves were the first team to go close, with top scorer Steven Fletcher shooting straight at Shay Given from Edwards' cross, but it was Villa who took the lead through Bent.
The England striker caught Christophe Berra in possession in the Wolves box and when the Scottish centre-back brough him down, Bent converted the ensuing penalty to register his 99th Premier League goal.
Wolves' response was quick in coming and within 10 minutes they were level, with Kightly curling a fine shot past Given after a wonderful piece of skill in the build-up from on-loan Arsenal midfielder Emmanuel Frimpong.
Karl Henry saw a volley headed off the line by Marc Alrighton and Given saved from David Edwards before the hosts went ahead in the 31st minute.
Kightly's corner was flicked on by Roger Johnson and Welsh midfielder Edwards reacted smartly to head the ball home.
Wolves have recovered a league-high 10 points from losing positions this season but Villa dragged themselves level six minutes into the second period when Keane swivelled and sent a shot past Wayne Hennessey after a corner was only partially cleared.
There was a long delay mid-way through the second half when Frimpong had to be taken off after being inadvertently kicked in the head by Stiliyan Petrov at a Wolves corner.
The hosts' hopes of victory began to recede in the 74th minute when Henry was shown a straight red card for digging his heel into Albrighton's torso during a midfield tussle.
Wolves held out for 10 minutes but with six minutes remaining, a clearance fell to Keane on the edge of the box and he rattled a superb strike in off the crossbar to preserve Villa's 34-year unbeaten record at Molineux.
Keane, who began his professional career with Wolves, almost made it a hat-trick in the game's dying stages, but his 25-yard drive swerved the wrong side of the upright.