Neil Shipperley scored twice to keep Neil Warnock's promotion chasers in touch with Championship leaders Reading.
He took his season's tally to eight, scoring in each half as Sheffield United overran Steve Cotterill's improving Burnley side, who had suffered just one defeat in their last seven games.
United, 2-1 winners at Turf Moor in August, forced the early pace, the lively Danny Webber producing two shots smothered on the line by Brian Jensen.
Midfielder Alan Quinn saw his drive from the edge of the area deflected by Micah Hyde, the ball spinning inches over the bar before centre-back Leigh Bromby almost broke the deadlock, his back header being blocked by the keeper.
Ade Akinbiyi, a target for Warnock last February, caught United on the break in the 22nd minute as he chased a Garreth O'Connor pass. The big striker cut inside finishing with a low shot that was pushed around the post by Paddy Kenny.
Shipperley took advantage of a mistake by Hyde drilling the ball across the face of the goal and inches wide of the target before the ex-Crystal Palace striker snatched the lead in the 29th minute.
Webber carved out the opportunity with another darting run into the area before Shipperley took over, turning quickly to crack the ball into the top right-hand corner from 15 yards.
Burnley defender John McGreal saw his close-range header scooped off the line by Kenny before the Sheffield side added a second on 35 minutes.
Nick Montgomery's cross from the right flank was met by centre-back Craig Short, whose far-post header was finished off from close range by Webber.
Webber was foiled by Jensen and Shipperley then squandered a chance to kill off the Lancashire side, heading Quinn's teasing cross wide from six yards.
The hardworking Webber was kept out by Jensen, who finger-tipped his fierce effort over the top before Shipperley grabbed his second.
Chris Armstrong, making his first start of the season after two injury-plagued years, whipped in an inch-perfect cross from the left and the big forward had time to control the ball before slamming a low strike beyond Jensen's reach from 16 yards.