Livingston's second consecutive win keeps alive the unlikely dream of staying in the Premier League.
Two weeks ago it looked impossible, but John Robertson's side can really give themselves a chance by beating Dunfermline next week.
They performed heroics to avoid the drop last season, and if they can keep up the level of this performance it would be a brave man who bets against them repeating the feat.
They got off to the perfect start with a goal after eight minutes. Craig Samson and Garry Kenneth got in a terrible mix-up chasing Colin Healy's through ball, and Sam Morrow nipped in between them to slot home a simple goal.
But against the run off play United equalised after 19 minutes when Charlie Mulgrew's cross was flicked home at the near post by David Robertson.
Livingston had more desire to win the game and deservedly went back in front four minutes after the interval, but again they had some dreadful defending to thank for the goal.
Richard Brittain's deep cross looked easy for Samson to gather, but he collided with David McCracken and the ball fell to Harald Pinxten four yards out to tap into the empty net.
United then enjoyed their best spell, and Roddie McKenzie made a couple of fine saves to deny Mulgrew and Colin Samuel.
But Livi wrapped up the points in the final minute with a penalty. Substitute Steve Hislop was bundled over by Alan Archibald, and Brittain stepped up to slam home the spot-kick that keeps Livingston's Premier League dreams alive.