A header from Peter Hartley, a Liam Donnelly penalty and a terrific driven effort from Chris Long earned the visitors a deserved three points.
Hamilton, whose goal also came from a penalty - converted by Ross Cunningham - lost Jamie Hamilton to a red card after just 20 minutes and never really recovered.
Boss Brian Rice had made just the one change from their previous match against Kilmarnock, with George Stanger coming in for Scott McMann.
Motherwell made two changes from their defeat to Hearts. In came Hartley and Long, with Richard Tait and Jermaine Hylton dropping out of the starting line-up.
It was the visitors who started the brighter of the two sides. Sherwin Seedorf darted into the box and unleashed a shot that Owain Fon Williams did well to push away, before Liam Polworth tried his luck with a right-footed shot that drifted just wide.
Motherwell continued to crank up the pressure and Long struck the crossbar from a Polworth corner before a third dead-ball delivery in succession brought about a goal, with Hartley placing his header past Fon Williams to put the visitors in front in the 16th minute.
It got worse for the home side just two minutes later. Jamie Hamilton blocked Polworth's goalbound header with his hand and was sent off by referee Andrew Dallas. Donnelly placed his penalty just beyond the reach of the diving goalkeeper.
It was looking grim for Accies but they grabbed a goal back from another penalty soon after.
Hartley was adjudged to have handled on this occasion and Cunningham lashed home the spot-kick in the 24th minute.
Hamilton regrouped by pushing Alex Gogic back into defence and then again at half-time by bringing on Mickel Miller. But before they could try to push for an equaliser, they found themselves two goals behind again.
Long did it all himself, running down the right wing before firing a shot across the face of the goal that nestled in the far corner of the net.
Hamilton tried to chase the game once more with Marios Ogkmpoe sent on up front but they failed to create another chance of note as Motherwell coasted to a comfortable derby win.