Skipper Vlaar said the home fans helped the team dig deep against Manuel Pellegrini's men.
"You could feel that happiness in the stands because they kept us going and we had so much energy, it was amazing," he told Villa's website.
"I am really proud and I think everybody is proud. We worked really hard to get the result and to make sure of our first home win.
"Coming back from a goal behind twice and to win at the end it was unbelievable - really, really great.
"To win against Man City at home is not easy but the gaffer always says on any given day you can beat them and this was the day."
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