Having enjoyed a 4-0 win over Stuart McCall's men in November, Ryan Dow gave Dundee an early lead in the first Scottish Premiership game of the weekend.
Gavin Gunning, who spent time on loan at Motherwell in 2011, doubled the advantage before the break and he went on to complete his brace shortly after half-time with a deflected free-kick.
Gunning doubled the hosts' lead five minutes before the break courtesy of some slack Motherwell defending that will no doubt have frustrated McCall.
After a flick-on from a corner, the unmarked Gunning was able to divert the ball home from close range to hand Dundee a two-goal cushion at the break.
Gunning's free-kick made it 3-0 after just two minutes of the second half, with the former Blackburn Rovers man enjoying a slice of luck as his strike took a deflection off a visiting defender and beat Nielsen - crashing in off his right-hand post.
Sutton pulled a goal back from the spot after soon after, after referee Bobby Madden spotted a handball in the area, but it failed to lead to a further fightback.
Dundee move within six points of Motherwell and boost their hopes of securing a top-half berth come the end of the season.
