The Brewers were good value for their half-time lead but tamely surrendered two goals in as many minutes in the second period as Aldershot climbed out of the bottom two.
Burton controlled much of the first half, winning seven of their eight corners, but wayward finishing allowed Aldershot to escape relatively lightly.
Andy Todd was the biggest culprit for the home team with a series of shots that flew high and wide, but the midfielder finally got it right in the 30th minute.
Player-manager Nigel Clough slipped a free-kick into the area and Todd outsmarted his marker before lashing home a right-foot shot from eight yards.
The Shots could have been level right at the end of the half but a shot from Tim Sills was superbly parried by Dan Crane and better still was Andy Corbett's goal-line clearance to deny Chris McPhee.
But Burton lost their momentum in the second half and defensive errors were punished by the Shots.
The visitors drew level in the 65th minute when poor play by Aaron Webster allowed Gary Holloway to hook the ball to the far post where Sills scored with a powerful header.
The Burton defence froze two minutes later when Stephen Reed lifted the ball into the area and, as there was no challenge, Nick Crittenden was allowed to squeeze the ball past Crane from eight yards.
It was not until stoppage time that Burton threatened to score an equaliser, but Webster lashed a left-foot shot too high and Darren Stride's header was well held by Nikki Bull.