Topscorer Benteke started the season in fine form, scoring five goals in his first five games, but he limped off during last weekend's 1-0 win at Norwich City.
It has since been confirmed that he will be sidelined for up to six weeks.
Many fans and pundits have suggested that Villa would struggle to score goals in the Belgian's absence. However, Karim El Ahmadi, Leandro Bacuna and Andreas Weimann helped to silence those doubters by finding the net to overcome the 2012 champions of England.
Vlaar told BBC Sport: "It is an unbelievable feeling. It was a great game, to come back two times from a goal behind with the spirit and energy we had, and with the fans behind us, was great and important as well. We just kept going.
"Man City are a strong team, we knew what they did [in beating Manchester United 4-1] last week. But even without Christian Benteke, who everybody knows is a very important player for us, we can still beat them - it is a big boost."
The win saw Villa climb up to ninth in the Premier League table.