The on-loan 19-year-old fired home from 20 yards in the 56th minute to give the Mariners the lead on his home debut. Adam Proudlock made it two from the spot after 72 minutes and then Dean Sinclair crashed home the third seven minutes from the end.
Danny Harrison headed narrowly over from a Jamie Green cross as Rotherham made the early running, but Grimsby responded with a Nathan Jarman shot which Andy Warrington tipped over, and the keeper then did well to keep out a Rob Atkinson header.
Warrington was beaten in added time by a superb 25-yard strike from Proudlock which came back into play off the far post.
Widdowson, set free on the left by Stuart Elliott, fired home an angled drive into the far corner for the opener.
Proudlock rammed home the penalty after having his shirt pulled by Nick Fenton before Sinclair exchanged passes with Elliott and crashed home the third.