United had some decent chances towards the end of a scrappy first half in Saturday's SPL encounter but Darren Randolph saved well from John Rankin and Jon Daly in quick succession.
Motherwell pushed United back for much of the second half but the visitors defended their penalty box resolutely.
Several hundred Motherwell fans braved the cold and rain to attend a pre-match ceremony to unveil artwork paying tribute to former captain Phil O'Donnell, who died almost four years ago after collapsing during a game against United.
But the weather proved more of a problem on the park with the wind affecting the flow of the game, although both sides tried to pass the ball throughout.
Motherwell retain a solid grip on third place and have still only lost to St Johnstone outside the Old Firm but they struggled for a cutting edge as they failed to add to their six home goals in the SPL, with Omar Daley unable to make an impact after retaining his place following his winner at Aberdeen.
United got the first effort on target but it came from inside their own half as John Rankin tried and failed to catch Randolph off his line.
Motherwell's first chance fell to Michael Higdon just outside the box following Randolph's long kick but his shot appeared to be heading wide before Dusan Pernis made sure. Randolph then held a decent drive from Gary Mackay-Steven.
United manager Peter Houston had vowed not to be so "kamikaze" after suffering four defeats at Fir Park last season but his side were almost caught on the break on the half hour.
Nicky Law released Chris Humphrey after Motherwell cleared a corner but United recovered to get men behind the ball and the move ended with Keith Lasley volleying over from a difficult chance.
Higdon tapped the ball in the net in the 35th minute after Garry Kenneth had stretched to stab Humphrey's low cross against his own post but the ball had gone over the line before the winger crossed.
United threatened several times before the break. Randolph pushed away Rankin's volley after a corner and then parried Jon Daly's curling effort after Shaun Hutchinson had misjudged a high ball. The goalkeeper then held Kenneth's looping header following another corner.
Motherwell stepped up a gear after half-time with Humphrey and Tom Hateley putting in some dangerous crosses.
Pernis held Hutchinson's header right on his line following Stevie Hammell's corner and, although Rankin had a shot saved at the other end, Motherwell continued to make most of the running.
United were getting men behind the ball though and Houston brought on defender Sean Dillon for front player Johnny Russell on the hour mark. Dillon, making his comeback from a calf injury, lined up in central midfield.
Kenneth could not get enough purchase on his back post header to beat Randolph from Willo Flood's corner and Steve Jennings saved Motherwell with a brilliant last-ditch sliding challenge on Rankin after United sub Lauri Dalla Valle had got away from Hutchinson, who pulled up injured and was soon replaced by Jonathan Page.
Substitute Jamie Murphy had a low strike saved after leading the resulting counter-attack and Motherwell pushed forward without success in the closing stages.
Rankin twice threatened to snatch a late winner but slid wide from Scott Robertson's low cross before Randolph saved his bouncing long-range effort.