The result left Jimmy Floyd Hasselbaink's side a point clear at the top of Sky Bet League One after second-placed Walsall beat Scunthorpe.
Neither goal was seriously threatened in a stifling first half.
United goalkeeper Mark Howard was tested only by Nasser El Khayati's 20-yard shot in the 26th minute, while Burton stopper Jon McLaughlin was happy to watch Chris Basham glance a header wide of the far post.
The visitors produced a spell of probing pressure after the break, with Billy Sharp's shot unluckily skidding over the crossbar, off the head of Burton skipper John Mousinho.
The hosts hit back with the move of the game - only for El Khayati to fire narrowly over from 12 yards.
Sharp, looking to add to this six-goal tally, was denied by the legs of McLaughlin and also had a shot deflected wide.
Mousinho might have snatched the decisive goal nine minutes from the end but fired over from El Khayati's corner.
McLaughlin got down well to push wide a low shot from United substitute Martyn Woolford to ensure the game ended goalless.