The visitors took the lead after 11 minutes when Stuart Beavon met Damien McCrory’s cross and beat Cambridge goalkeeper Will Norris with a thumping header.
Cambridge drew level in the 25th minute when Tom Elliott headed home Sullay Kaikai’s free-kick from the right.
Burton were denied a penalty immediately after half-time when Beavon looked to have been brought down by Josh Coulson but the referee awarded only a corner.
Cambridge were handed the initiative in the 67th minute when Harrison Dunk raced through on goal and was felled by goalkeeper Jon McLauglin.
McLaughlin was dismissed and Robbie Simpson powered the resulting penalty past replacement goalkeeper Scott Shearer.
Burton drew level again 13 minutes from the end through right-back Phil Edwards, who received a short free-kick and struck a magnificent effort into the top corner from 30 yards.
And Burton won the game with two minutes to play when Norris could only palm a cross into the path of substitute Kevin Stewart, who slotted home.