Manchester United had extended their lead at the top to 15 points with a 4-0 victory over Norwich City on Saturday, while Tottenham Hotspur and Chelsea also won at the weekend to close in on second place.
But City responded well at Villa Park as a Carlos Tevez goal in the 45th minute proved to be the difference between the sides.
Yaya Toure was thrilled to keep the pressure on United and echoed his manager's view that City could still emerge as Premier League champions.
"There was quite big pressure and I think today we needed to deliver," he told Sky Sports.
"Villa played very well in the first half but after that I think we managed and it was a great three points.
"Today we showed we have a fantastic squad, we are sad with Jack (Rodwell, who went off injured), but this is an important day for us.
"Twelve points is a lot but it's not finished."
Kolo Toure, who was impressive in defence, added: "It was really important for us to win this game because there are teams coming behind us and we need to be able to deal with that.
"I'm doing my best for me, I love football and every time I have the chance I will give 100 per cent."