Motherwell started the game brightly and created a couple of half chances with Calum Elliot heading over and Scott McDonald shooting wide from 18 yards.
Well continued to dominate and were presented with a great opportunity on the half-hour mark. Roddy McKenzie dropped a Brian Kerr corner and the ball fell to Mark Reynolds but his header was cleared off the line.
Well continued to push forward and further chances fell to Eliot, Richie Foran and Jamie Paterson but none of them really troubled the visiting keeper.
Fifteen minutes after the restart Well got the break they were looking for when Reynolds' initial effort was saved by McKenzie. Reynolds kept the ball in rather than accept another corner and laid the ball to McDonald who shot low past keeper and defender on the line.
Dunfermline responded and found an equaliser with their first effort at goal eight minutes later. Jim Hamilton played in Stevie Crawford who fired across Colin Meldrum and in off the far post.
Well took the lead again with seven minutes left when McDonald gathered a Paul Quinn pass before laying off to Clarkson and the substitute fired low past the keeper from 18 yards.