Livingston racked up their second consecutive home win to keep alive hopes of avoiding relegation.
Livingston secured just their fourth win of the season
Sam Morrow took advantage of some hesitancy from goalkeeper Craig Samson to shoot Livingston into an early lead.
United teenager David Robertson scored an equaliser when he flicked home a low Charlie Mulgrew cross at the near post.
But Samson clattered into team-mate David McCracken, allowing Harald Pinxten an easy tap-in and Richard Brittain added a late penalty.
Livingston are now six points behind 11th-placed Dunfermline, with four games remaining.
The home side started buoyantly and right-back David Mackay tested Samson with a shot from 15 yards which was comfortably gathered.
But the young 'keeper was beaten after eight minutes when he and defender Garry Kenneth both left a Colin Healy pass and Morrow capitalised on the confusion, to beat Samson in a challenge and then shoot into an unguarded net.
The striker, on loan from Hibs, then tried his luck from 20 yards, only to be denied by Samson who tipped the ball around the post at full stretch.
Livingston were making all the running but the visitors grabbed an equaliser when Mulgrew's cross was glanced in by Robertson.
Livingston responded to the setback with a Morrow drive on the half-volley which flew into the side-netting.
Both goalscorers continued to have an impact on proceedings and home goalkeeper Roddy McKenzie had to race from his goal to prevent Collin Samuel latching on to a clever through ball from 19-year-old Robertson.
United's Stuart Duff sent a looping effort just wide, while Samuel could not direct a shot from an acute angle on target after some impressive work from Mulgrew.
The second half was only four minutes old when another defensive mix-up was punished by Livingston.
Wes Hoolahan's cross created confusion in the area and when McCracken collided with Samson, Pinxten was afforded the luxury of shooting into an empty net from barely two yards out.
Healy then smashed in a volley at goal from 20 yards, but Samson was on hand to produce a smart save low to his right.
The away side were looking sluggish but finally Barry Robson broke forward to flash a shot wide from just outside the penalty box.
Livingston goalkeeper McKenzie was then called into action and he produced a magnificent save in pushing a curling Mulgrew free-kick from distance over the bar.
Robson wasted a great opportunity to net an equaliser when he blasted a cut back from Samuel over the bar from 16 yards out.
But Livi were not to be denied and after Alan Archibald hauled down substitute Steve Hislop, Brittain confidently converted the spot kick to secure only the Lions' fourth win of the season.
Livingston: McKenzie, McNamee, Pinxten, Strong, Mackay, Brittain, Walker (Tierney 90), Healy, Hoolahan (Adams 76), Morrow, Whelan (Hislop 75). Subs Not Used: Roy, Snodgrass, Miller, Dorrans.
Booked: Walker, Whelan. Goals: Morrow 8, Pinxten 49, Brittain 90 pen.
Dundee Utd: Samson, McCracken, Archibald, Kenneth (Ritchie 59), Mulgrew, Duff, Kerr, Brebner, Robson, Samuel, Robertson. Subs Not Used: McLean, Cameron, Gardiner, Abbot, Easton, Goodwillie.
Booked: Robertson, Ritchie. Goal: Robertson 19.
Ref: B Winter