The hosts suffered a second successive home defeat as Ricky Holmes and Simon Ferry made the most of some indifferent defending.
The victory was marred only by an 84th-minute red card for full-back Yassin Moutaouakil for taking a kick at Burton winger Jimmy Phillips before Zander Diamond bagged a late consolation goal for Albion.
Pompey could have been in front in the eighth minute but Jed Wallace was denied by the legs of goalkeeper Jordan Pickford from six yards out.
The visitors looked the more creative side and took the lead in the 33rd minute. Pickford did well to keep out a Patrick Agyemang header, but Holmes reacted quickly to hook home the loose ball from a tight angle.
Only a stunning one-handed save by Pickford kept Andy Barcham off the scoresheet as Burton suffered more defensive jitters.
Pompey keeper John Sullivan had to get his fingertips to Adam McGurk's dipping 25-yard shot but the visitors were good value for their half-time lead.
Ferry increased the advantage six minutes after the break when he stabbed in a close-range shot after a Holmes effort had been partially saved by the overworked Pickford.
Defender Diamond pulled one back for Burton in the fifth minute of added time but it was too little too late.