The striker, who was sent to Villa on loan from the LA Galaxy earlier this month, recorded his first two goals with the team while playing against one of his former squads.
The 31-year-old striker tied the game in the 51st minute before hitting a late winner to give Aston Villa its third road victory of the season.
"Robbie's done that throughout his career," said Villa coach Alex McCleish. "It was no surprise seeing him getting on the scoresheet."
Darren Bent opened the scoring in the 11th minute to give Villa the early lead. But back-to-back goals from Michael Kightly and David Edwards gave Wolves the advantage going into halftime.
Keane's first goal was scored just moments into the second half when he shot from 25 yards out after a corner was only slightly cleared. The Irishman, who began his career at Wolves, refused to celebrate.
"It was spectacular," McCleish said. "Not many people shoot from outside the box these days, but Keane has done that a few times over the years."
With 15 minutes left to play, Wolves were down to only 10 men after Karl Henry was sent off with a red card. They would hold their own for only a few minutes, however, as Keane slapped home a stunning strike from 20 yards in the 85th minute.
Keane signed a two-month loan with Villa with the hopes of remaining in playing shape heading into the MLS season and Euro 2012.