The big striker ended stubborn resistance in the 80th minute after City had to battle against the odds following the dismissal of Ricky Ravenhill and the loss of centre-halves Luke Oliver and Andrew Davies to injury.
Visiting skipper Ravenhill was given his marching orders by referee Andy D'Urso in the 32nd minute of an otherwise tepid first half for violent conduct after a clash in the centre circle with Burton midfielder Lee Bell.
The first real chance of the game fell to the visitors in the 40th minute when a James Hanson header was deflected narrowly wide. Billy Kee should then have put Burton in front in added time at the end of the first half but poked a Damien McCrory cross wide.
The Brewers almost made their extra man count in the 55th minute when Jacques Maghoma's shot came back off the crossbar. Kee then missed an even better chance to break the stalemate when he headed wide from close range in the 78th minute.
But Zola made no mistake when he met McCrory's cross with a dividing header inside the far post.