Second-half goals from Alfie Potter and Danny Rose secured the victory that kept Chris Wilder's side - also unbeaten - in second place.
A tight and chanceless game exploded into life in the 34th minute when Sharps was given his marching orders for taking a kick at striker Dave Kitson.
Kitson - already booked twice this season - was perhaps lucky to escape with a yellow card after pushing over the Burton defender in retaliation.
Potter put the U's in front with solo goal in the 49th minute, tricking his way past three opponents before ramming a deflected shot into the far corner.
Only a superb save by Dean Lyness denied Tom Newey a second goal for the visitors and the Burton keeper was also tested by Asa Hall's firm shot.
Burton fought hard to get back into the game, but substitute Jimmy Phillips' shot was blocked by team-mate Adam Reed, who was then too high with an overhead kick.
Rose sealed the three points for the visitors when he bundled home Ryan Williams's cross in the 85th minute.