Beattie's strike partner Billy Sharp also found the back of the net with a well-placed header and United were able to hang on for three vital points, despite a late Clarets rally which included a typical poacher's goal for veteran Andrew Cole.
Beattie had already seen a great header tipped over by Brian Jensen before opening the scoring with a ferocious free-kick from fully 30 yards after ex-Blade David Unsworth had needlessly fouled David Cotterill.
Burnley responded with Kyle Lafferty being denied by the sharp reflexes of Paddy Kenny after good work on the right by Cole. James O'Connor also went close to an equaliser with a speculative shot from 20 yards.
The home side, now surely out of the play-off reckoning, made a bright start to the second half too, with Robbie Blake and Lafferty both having shots blocked.
But there was always more of a cutting edge about the visitors and it was no surprise when Sharp placed a header into the bottom corner after the outstanding Cotterill had skipped past Stephen Jordan before delivering a perfect cross.
Beattie, United's record signing, almost added a third but his header from a right-wing corner flashed inches wide.
Ten minutes from time Burnley pulled themselves back into the picture when Cole picked up a pass from substitute Joey Gudjonsson before turning smartly to place a right-foot shot beyond Kenny.
The Blades keeper then reacted brilliantly to deny Cole an equaliser in a goalmouth scramble as Burnley went in search of a point.