Dunne had put Villa ahead early on with his first goal for Martin O'Neill's team since his five million pounds switch from City in August.
But Welsh star Bellamy continued his impressive start to the season with a clinically taken equaliser after the break at Villa Park to lift City into fourth place.
After losing a seven-goal thriller at Manchester United in their last away fixture, it was essential for Mark Hughes's expensively assembled side to emerge unscathed from another tough trip and City's battling display bodes well for their hopes of earning a Champions League place.
They will go into the international break ahead of Arsenal and Liverpool and only five points behind leaders Chelsea with a game in hand, while seventh placed Villa, who also harbour ambitions of a top four finish, deserve credit for an enterprising display.
Hughes handed an immediate recall to Emmanuel Adebayor after the Togo striker's three-match suspension for violent conduct against his former Arsenal team-mate Robin van Persie.
But it was City midfielder Gareth Barry who commanded the spotlight in the early stages as the England star made his first return to Villa since joining Hughes's team for 12 million pounds in the close-season.
Barry spent 11 years with Villa but had been keen to leave for some while so inevitably he received a hostile reception from the home fans.
Villa almost took a second-minute lead when Gabriel Agbonlahor flicked Ashley Young's low corner goalwards, only for City keeper Shay Given to make a fine stop with his foot.
Wayne Bridge led City's response as the left-back's shot deflected over the crossbar before Adebayor brought Brad Friedel into action.
But Villa were causing problems for the City defence and Stiliyan Petrov shot just wide with a long-range drive.
Barry wasn't the only player coming up against his former employers.
Republic of Ireland defender Dunne joined Villa from City just before the transfer deadline and was fiercely critical of the club's chief executive Garry Cook, who angered him by claiming unglamorous players like Dunne didn't fit into the club's new global image.
He got his revenge in emphatic fashion in the 15th minute. Stephen Warnock curled over a teasing corner and Dunne rose above Barry to power a header past Given.
Dunne could have been forgiven for rubbing it in but he refused to celebrate the goal as a mark of respect to City's supporters and his gesture was applauded by those who travelled from Manchester.
Barry almost laid on an equaliser for City just before half-time as Adebayor rose to meet the midfielder's free-kick with a header that Friedel tipped over.
Villa created chances without applying the finishing touch early in the second half. Warnock had a shot blocked by Joleon Lescott before Milner lashed a powerful shot across the face of goal.
Dunne could have scored again from another set-piece, but his header from Milner's corner flashed past the far post.
City had won five of their first six league matches thanks in large part to their impressive firepower up front and two of Hughes's forwards combined to work their side's 67th-minute equaliser.
Stephen Ireland, on as a substitute, slipped a pass through to Adebayor down the right side of the Villa penalty area and his cutback was perfectly weighted for Bellamy to sweep past Friedel for his fourth goal of the season.