For the second festive fixture in three days they also had a man sent off with Jim Hamilton being punished near the end for using an elbow.
Poor finishing is dragging Dunfermline down to Division One, although they carved out enough chances to have buried Motherwell by half-time.
Flying winger Frederic Daquin saw an early shot blocked and then fired in a teasing cross which was not attacked in the six-yard box.
Striker Mark Burchill was unlucky when his hooked effort rattled the woodwork after 12 minutes and four minutes later Martyn Corrigan cleared a Phil McGuire header off the line.
Scott Muirhead tested Graeme Smith and Darren Smith survived a penalty appeal as Dunfermline kept pressing, but Motherwell stunned the home support by scoring out of the blue.
Souleymane Bamba momentarily took his eye off the ball and Marc Fitzpatrick produced an assured left-foot finish.
Darren Smith missed a simple chance to make it 2-0, but Dunfermline quickly established control with Bamba and Burchill going close before half-time.
Burchill wasted a terrific opportunity to equalise moments after the break before Muirhead somehow contrived to miss an even easier chance.
Scott McDonald showed how it should be done with a stunning 20-yard drive to confirm Motherwell's win with 12 minutes left and he nearly struck again at the death as Dunfermline disintegrated following Hamilton's dismissal.