Dunne had given Villa a half-time lead with his first goal since his £6million move from Eastlands, outjumping former Villa midfielder Gareth Barry.
But Bellamy rescued a deserved point for Mark Hughes' side midway through the second period.
Former City skipper Dunne headed Villa into the lead after 14 minutes, getting on the end of Stephen Warnock's corner to climb above Barry and head back across Shay Given.
Dunne went close again, while Emmanuel Adebayor threatened for City before Bellamy equalised after 67 minutes.
Shaun Wright-Phillips released Stephen Ireland who then played the ball into Adebayor down the channel, and he cut the ball back to Bellamy who hammered home from 12 yards.