Norwich took the lead after just three minutes of the Premier League clash through Wes Hoolahan but Benteke equalised after an acrobatic finish from a Vlaar cross on 25 minutes.
Benteke grabbed a second minutes later before a Leandro Bacuna strike and an own goal from Sebastien Bassong made the game safe for Villa before half-time.
Vlaar praised Benteke for his part in the comeback, insisting it was a much-needed victory for Paul Lambert's men.
"We made a few changes and then came the goal," Vlaar told Sky Sports. "We didn't start that well and then were 1-0 down and the big man has showed what he's capable of. He was really important for us.
"We didn't score many goals the last few games but today it all fell right for us and we really needed it for ourselves and for everybody else who loves Aston Villa."
Benteke, who had not scored in Villa's previous four matches, added: "We started really badly and made some changes and got the first goal and it was good for the team.
"Since we scored the first goal, we really showed some good football and some good character as well.
"(Scoring the goals) is good for myself but more important for the team."