A late goal from Gary Phillips earned Rovers their first major victory over their Lanarkshire neighbours as they defied odds of 16/1 to triumph on neutral territory at New Douglas Park.
The team sitting third bottom of the Scottish Professional Football League shocked the side who are third top when Phillips struck a first-time effort from 18 yards.
Motherwell found Rovers difficult to break down from the start with Bob McHugh curling their first decent attempt on goal wide from 25 yards.
Well goalkeeper Gunnar Nielsen was then called into action with a superb fingertip save from Liam Cusack to prevent Albion from taking a surprise lead.
McHugh headed over as Motherwell regained control and Stuart Carswell then sliced wide from the edge of the area.
Albion's stubborn defence was still holding firm and Chris Dallas spurned another good chance to put them ahead when he blazed a shot over from Phillips' bouncing cross.
Paul Lawson and Carswell then sent efforts over the bar at the other end to leave the sides deadlocked at the half-time interval.
It was a similar story after the restart as Motherwell continued to toil for a breakthrough with Lawson's deflected shot looping into the arms of Rovers keeper Neil Parry.
Albion had another decent opportunity to take the lead when Mark McGuigan turned Steven Hammell before firing narrowly wide.
Motherwell pressed hard for a winner in the closing stages with Parry saving John Sutton's powerful close-range header.
But Albion continued to defend stoutly and they stunned Motherwell when Phillips fired a left-foot shot into the corner of the net after he was teed up by Ryan Tiffney.
Henri Anier had a good chance to level for Well in injury-time when the ball fell for him in the box but he sliced wide.