Both sides stuck with the teams that had turned out in midweek when United drew with Hearts and Motherwell lost at Kilmarnock.
The first time a keeper was called into the action was in the seventh minute when Derek Stillie saved Alan McCormack's 20-yard pile-driver, and 13 minutes later Graeme Smith was called upon to do the same when he kept out Barry Robson's stinging drive.
Motherwell opened the scoring on 26 minutes when Richie Foran galloped on to a Scott McDonald pass down the left flank, held off the challenge of Brian Kerr before firing an angled drive low past Stillie.
The remainder of the first half was poor fare as neither side could find any rhythm with the game being riddled by mistakes.
United started the second half the better side with Robson's free-kicks causing havoc in the Well box. Alan Archibald saw a shot skid wide with one of them.
But the Steelmen doubled their lead in the 56th minute when Foran headed home a Kerr corner at the back post.
Well continued to create the better chances with McCormack being denied by
Stillie on the break and Steven Hammell seeing a free-kick bounce clear off the base of the post with Stillie beaten.
The home side managed to hold on for their first win of 2006 without any late drama.