Zola doubled Burton's advantage six minutes later when he cut in from the left and curled his shot into the net past goalkeeper Jon McLaughlin.
However, hosts Bradford came back strongly into the contest and halved the deficit on 35 minutes from the penalty spot.
However, Burton regained their two-goal advantage on 44 minutes, Robbie Weir latching on to Alex McDonald's pass in the middle of the Bradford box before shooting home past McLaughlin at the near post.
The visitors had a chance to make it 4-1 in the opening minutes of the second half, but Maghoma's free kick went high over the crossbar.
Then just before the hour mark John McGrath saw his shot from 25 yards comfortably pushed away by McLaughlan.
Bradford did pull one back and made it 3-2 in the 73rd minute through Thompson, who drove home from just outside the box after cutting inside onto his left foot.
MacDonald could have added to Burton's tally just four minutes later had his effort not rattled the crossbar.