Having missed a hat-trick of first-half chances, Baldock found the roof of the net from close range on 12 minutes after the break and then forced the ball over the line on 76 minutes after the Dons had failed to deal with a corner.
Shaun Williams had shot the visitors ahead on 17 minutes, chesting the ball past City debutant Adam El-Abd and firing past Elliott Parish.
More poor defending gifted to the Dons their second as Ben Reeves was given the freedom of Ashton Gate to run onto Samir Carruthers' through-ball and chip over the advancing Parish.
Rovers made and squandered five gilt-edged first half opportunities, with skipper Baldock heading wide of an open goal and twice failing to beat goalkeeper David Martin in one-on-one situations.
Jay Emmanuel-Thomas and Greg Cunningham should also have scored, while Daniel Powell and Dean Lewington were guilty of wayward finishing for the Dons.