In fact the first half was best forgotten. United's best chance came in the 38th minute when a teasing James O'Brien ball left Noel Hunt and Christian Kalvenes challenging each other to net, but they collided and the ball was cleared.
This was immediately followed by Motherwell's only clear chance of the half, when a neat combination of Keith Lasley and Chris Porter left the ball at the feet of Ross McCormack, but the striker blasted over from 14 yards.
A wonderful O'Brien free-kick opened the second period with Garry Kenneth somehow heading wide with a goal at his mercy.
But the pattern and the quality of the game was a mirror of the first period with only flashes of entertaining football. One came in the 59th minute when McCormack brilliantly controlled the ball, but just as he was about to pull the trigger, a superb challenge from Michael Kovacevic prevented the opener.
Mark De Vries went close with a shot in the 65th minute but it flashed past the post then another piece of magic from McCormack four minutes later saw the striker set up David Clarkson, but Lukasz Zaluska produced the save of the match with his feet.
With United struggling, manager Craig Levein made an inspired substitution bringing on Danny Swanson for O'Brien and the sub scored a cracker within a minute of being on the pitch.
Latching on to a Willo Flood ball, he weaved past two defenders before smacking it in off the far post from 12 yards.
And United wrapped it up in the 89th minute when Flood's through ball set up De Vries to run in on goal and round the keeper before coolly slotting home.