First-half goals from Alex Harris, Greg Stewart, Gary Irvine and an own-goal from Mark O’Brien in the second gave the Dark Blues a comfortable win, with John Sutton grabbing a consolation for the visitors who had Henrik Ojamaa sent off just before half-time.
Dundee took the lead with their first attack of the game when Harris found space on the left and unleashed a shot which deflected off Stephen McManus to wrong-foot Well goalkeeper Dan Twardzik.
The hosts doubled their lead inside ten minutes when Stewart nodded home from close-range after his initial shot had come back off the crossbar.
Stewart almost made it 3-0 straight after but Twardzik produced a wonderful diving save to turn aside his curling effort, which was destined for the top corner.
Motherwell pulled a goal back on 19 minutes when Sutton slotted home after good work from Josh Law and Ojamaa down the right-hand side.
The Dark Blues restored their two-goal advantage just after the half-hour mark when Irvine slammed the ball home after goalkeeper Twardzik dropped the ball following a Stewart corner.
Things went from bad to worse for the visitors on the stroke of half-time when Ojamaa was sent off for a late challenge on Kevin Thomson.
Motherwell conceded a fourth in calamitous fashion on 69 minutes when the ball trickled in off O’Brien after he and Twardzik collided in the box.
The final twenty minutes were uneventful as Motherwell engaged in damage limitation and Dundee seemed content with their three goal advantage.
The win sees Dundee move eight points clear of tenth-placed Motherwell, who lost their third straight league game.