John Sutton grabbed the winner for the visitors 18 minutes from time to break the resistance of St Mirren, who had Steven Thompson sent off early on.
Kenny McLean also had a goal controversially ruled out for the home side when his header appeared to cross the line.
Both sides had chances early on with Keith Lasley firing the ball wide from 20 yards, while at the other end Jason Naismith found himself through on goal but could not get his effort on target from a tight angle.
But the turning point came on 19 minutes when Buddies skipper Thompson was shown a straight red for a late challenge on Mark O’Brien.
Despite being a man down, the home side more than held their own with Jim Goodwin’s half-volley saved by Dan Twardzik.
Motherwell’s first shot on target came on the stroke of half-time when Josh Law’s half volley from the edge of the penalty area was comfortably saved.
Baraclough made two changes at the break with Lee Erwin and Fraser Kerr coming on.
But it was St Mirren who looked to have scored at the start of the half when McLean’s header struck the underside of the bar and appeared to bounce behind the line.
However, referee Alan Muir waved play on and Jim Goodwin’s drive flashed just wide of the far post as his team-mates were celebrating.
More controversy erupted a few minutes later when McLean’s penalty appeals were waved away after he was tripped in the area.
And Motherwell piled on the misery by scoring on 72 minutes when Sutton slotted the ball in from Law’s pass.
The win sees Well remain in 10th place in the table, while St Mirren stay rooted to the bottom.