Motherwell took a large step towards securing their Premiership status with this vital victory, which lifted them ten points clear of second-bottom Kilmarnock.
It also saw Mark McGhee’s men move into the top-six, although Dundee have the chance to reclaim sixth spot against Hearts today.
Unfortunately for United, their mini-revival came to an end at just the wrong time and they remain eight points adrift at the bottom of the table.
With both teams anxious for a victory, this was an open game from the first whistle, with United midfielder Paul Dixon lashing a shot into the side netting in the first attack.
Three minutes later United had a let-off when Scott McDonald failed to connect properly with Chris Cadden’s driven cross, allowing Polish goalkeeper Michal Szromnik to parry his first effort and smother his rebound attempt.
Henri Anier had already had a goal disallowed against his former employers by the time he opened the scoring with a stunning strike midway through the first half.
As so often, John Rankin provided the spadework but the spotlight deservedly fell on Anier, whose rising drive from 20 yards almost ripped the netting away.
Motherwell keeper Connor Ripley kept his side in contention on 29 minutes, diving to his left to keep out a netbound 30-yarder from Paul Dixon.
United played like a team scrapping for survival and Ripley saved well again, this time from Billy McKay.
McDonald was fortunate to escape punishment when he elbowed Coll Donaldson in the face and United’s sense of grievance was heightened when the defender was cautioned for dissent.
Worse was to follow for the visitors on the stroke of half-time when Ryan Dow was harshly penalised for a robust challenge on substitute Morgaro Gomis and Marvin Johnson’s header from Josh Law’s free-kick arced over Szromnik and into the goal.
The winger came close to putting the hosts ahead ten minutes after the restart when his left-foot drive was deflected on to the bar and over.
However, Johnson claimed the assist when Motherwell moved ahead. He latched on to a perfectly-weighted through ball from McDonald and his driven cross was forced home from point-blank range by Louis Moult.
United were deflated by that and rarely looked like levelling. Motherwell, indeed, were the more dangerous on the counter-attack and Paul Paton was shown a yellow card but, in truth, was fortunate to remain on the park for a lunge from behind at Gomis.
Motherwell: Ripley, Law (Kennedy 87), Hall, McManus, Hammell, Cadden, Lasley (Thomas 63), Pearson (Gomis 34), Johnson, McDonald, Moult. Subs not used: Ainsworth, Fletcher, Samson, McFadden.
Dundee Utd: Szromnik, Donaldson, Morris, Gunning, Spittal, Rankin, Dow (Fraser 76), Paton, Dixon, Anier, McKay (Ofere 76). Subs not used: Dillon, Knoyle, Murray, Durnan, McGovern.