Goals from Stevie Crawford and James Grady in the first half took the game out of Livingston's reach as the home side failed to muster anything of note in the second half.
Livingston manager Richard Gough insisted this was a match his side could not afford to lose and they now face a long struggle to avoid relegation.
The game was an untidy affair with neither team able to string passes together with any consistency.
Colin McMenamin was booked for a clumsy challenge on United goalkeeper Tony Bullock early on and Grant Brebner was yellow carded shortly afterwards for a mistimed tackle on David McNamee.
But it was United who gained the upper hand when they took the lead after 14 minutes with a well-constructed goal.
Bullock's long clearance was headed on by Jim McIntyre and Billy Dodds fed Crawford who drilled a low left-foot shot past Roddy McKenzie.
Ten minutes later, McKenzie had to race from his line to hook the ball clear after Crawford out-sprinted Oscar Rubio after another long clearance from Bullock.
Livingston did not have a shot at goal until the 31st minute when Mark Wilson was wayward with a shot from the edge of the area.
United struck again four minutes from the break. Mark Wilson's corner was headed back across goal by Alan Archibald and Grady volleyed home at the far post.
Livingston came close to pulling a goal back moments later when Richard Brittain cut the ball back across goal and Eric Deloumeaux's 18-yard shot was just inches wide.
The home side had to do something an Richard Gough replaced Wilson and Brittain with Stephen Adam and Attila Kriston at half time.
It was United who continued to look the more threatening and Brebner was inches away from the third goal when he lofted the ball over McKenzie from the edge of the area but the ball struck the underside of the crossbar before bouncing to safety.
Adam carved out a chance for McMenamin after 62 minutes with a fine run down the left but the striker was always stretching for the ball and could not direct his header on target.
But United looked solid at the back for the most part with Archibald and Lee Mair forming a formidable partnership at the centre of their defence.
Burton O'Brien looked the one player capable of unlocking the United defence but he was kept well policed and the home side were bereft of ideas at times.
Substitute James McPake came close to pulling a goal back 13 minutes from time when he lobbed the ball over Bullock but it was just too high and it ended up on the roof of the net.