Aaron Webster gave the Brewers an early lead, with Jonny Dixon levelling for the Shots on half-time. The on-loan striker had seen his penalty well saved by Saul Deeney but the Wycombe man followed up well to hit the target.
Burton opened the scoring after only four minutes. Shots defender Greg Heald gave away a free-kick, which Kris Taylor floated in, and with Aldershot unable to clear their lines, Webster was alert to steer the ball past a helpless Nikki Bull.
Aldershot almost equalised through a Steve Watson piledriver on 16 minutes, which hit the upright and went away for a goal kick. Playing the better football, in the first half, the Brewers created an excellent opportunity to double the lead two minutes later, but Webster's cross was headed over the bar from a diving Taylor.
The shell-shocked Shots managed to re-group and with some free flowing football created further chances to draw level.
Nick Crittenden was denied by a fine Deeney save, the keeper getting down well to thwart the Aldershot midfielder and then, Dixon saw a smart turn and shot go straight at Deeney
Aldershot were on level terms in bizarre circumstances. A short corner in which Matt Somner and Ryan Williams exchanged passes, was floated into the danger zone.
Darren Tinson who until that point had had a commanding performance managed to somehow handle the ball as he attempted to clear it from a prostrate position; the referee had no hesitation in pointing to the spot.
Burton's delight at Deeney's save was short-lived as Dixon netted the rebound.
Both sides had some good chances to secure all three points, Gary Holloway was denied by Deeney's reflex save eight minutes from time, with Bull keeping out Taylor with a fine save a minute later.
With seconds remaining and with Burton hanging on, the lively Leroy Griffiths saw his powerful strike hit the crossbar, but the points shared was a fair result.