Dunne had given Villa a half-time lead with his first goal since his £6million move from Eastlands, outjumping City's former Villa midfielder Gareth Barry.
But the impressive Bellamy rescued a deserved point for Mark Hughes' side midway through the second period.
Villa had the better of the opening 45 minutes, but City were more menacing after the break. Gabriel Agbonlahor went close to giving Villa the lead after only two minutes from the first corner of the game, with his first time flick forcing a fine save from Shay Given.
Villa skipper Stiliyan Petrov then shot just wide with a low drive after being teed up by Ashley Young 20 yards out.
Then after 14 minutes former City skipper Dunne headed Villa into the lead. Stephen Warnock sent over an inswinging corner and Dunne was perfectly placed to climb above Barry and head back across Given.
City started to see more of the ball and Brad Friedel was seriously extended for the first time after 41 minutes, tipping over an Emmanuel Adebayor header.
Barry went close to setting up a City equaliser within two minutes of the start of the second half, with his probing pass only just failing to pick out Adebayor's run.
Dunne had a good chance to score for the second time but this time his header slid just wide. City forced a string of corners and after 67 minutes Bellamy brought them back on level terms with his fourth goal of the season.
Shaun Wright-Phillips released Stephen Ireland who then played the ball into Adebayor down the channel. He cut the ball back to Bellamy and he hammered the ball home from 12 yards.