The Dons thought they had taken an early lead when Craig Brewster's challenge on Jamie Paterson forced the makeshift right-back to turn the ball into his own net.
However, the referee had seen a little nudge from the veteran forward and disallowed the effort.
On 31 minutes the visitors did take the lead and Brewster was involved again as his clever header into the box forced Marc Fitzpatrick to stretch for it as Steve Lovell waited to pounce.
Unfortunately for the Well man, his touch looped the ball over his own keeper and into the net.
Five minutes later it took a fine save from keeper Graeme Smith to keep the home side in it.
Chris Clark's cross-cum-shot was cleared into the path of Jamie Smith by Mark Reynolds but Graeme Smith reacted well to beat out his effort.
Motherwell started the second half the brighter side and Scott McDonald was unlucky on two occasions, firstly shooting into the side-netting from an acute angle and then seeing a shot blocked by Russell Anderson.
The home side came close again after 63 minutes. This time McDonald was the provider as his cross picked out Krisztian Vadocz at the front post.
The Hungarian turned and shot in one movement only to see his shot crash off the inside of the post.
They were once again denied late on when Paul Keegan's flick was turned goalwards by McDonald only to be denied by a fine reflex save from Jamie Langfield.
The Dons sealed the points as the game headed to stoppage time courtesy of a stunning strike by Richard Foster from all of 30 yards as he latched on to a clearance from Vadocz and left Smith helpless with a first-time effort.