Goals from David Brown and Andrew Mangan extended Stanley's run to seven points from three games since back-to-back defeats against Exeter and Cambridge United.
The future looks less promising for Burton, however, after they failed to build on their defeat of Scarborough to slip worryingly close to the foot of the table.
Despite bursts of heavy pressure from the home team, Stanley were solid and dependable at the back and produced the extra quality needed to separate the teams in a tight game.
Brown gave them the lead in the ninth minute, starting a counter-attack in midfield and then continuing his run to rifle home Steve Jagielka's low cross from eight yards,
Stanley survived a goalmouth scramble after Darren Stride's far post header, but Andy Corbett had to make a goalline clearance in the 24th minute to prevent Gary Roberts from heading the visitors into a two-goal lead.
Burton's best spell came either side of the interval, but their finishing lacked confidence and conviction.
Before the break, Andy Todd miscued Keith Gilroy's cross to the far post and early in the second half another wave of pressure went unrewarded.
Loan signing Danny Bacon saw his close-range effort cleared off the line by Mike Flynn and Jon Shaw fired wide from eight yards after Bacon had cleverly overstepped Todd's cross from the right.
Todd screwed another chance wide before Stanley gave Burton another lesson in finishing to wrap up the points in the 72nd minute.
Leam Richardson's long ball forward was headed on by Paul Mullin and substitute Mangan raced cleared to beat Dan Crane with a precise low shot from just inside the area.
Stanley keeper Darren Randolph had his only testing save to make when he pushed a shot from Shaw to safety in the last minute.