Molyneux’s third of the season was enough for the Shrimps to leapfrog their opponents in the table, rising to 13th in League Two.
The margin of victory could have been greater with two goals ruled out for offside and a pair of efforts hitting the woodwork.
Nevertheless, with all the off-field dramas surrounding the club, 14 points from seven games so far this month represents nothing short of an excellent three-and-a-half weeks’ work.
Bentley had made three changes from the side which drew at Newport County in midweek.
Molyneux, Aaron McGowan and Antony Evans were back in the starting XI with Luke Conlan, Aaron Wildig and Rhys Turner the men to make way.
It looked an inspired decision when the Shrimps took the lead with only 86 seconds gone.
Paul Mullin forced Town skipper Shaun Pearson to concede a corner; instead of a ball into the area, Michael Rose pulled the ball back to Molyneux for a 20-yard, first-time effort beyond James McKeown.
With the rain falling, a strong breeze and a less than perfect area in front of the dugouts, it was never going to be a match full of free-flowing football.
Shrimps’ keeper Barry Roche was well positioned to hold Gavin Gunning’s header and saw Danny Andrew’s free-kick drift wide as both sides got to grips with the conditions.
Andy Fleming’s shot was cleared by Town’s Chris Clements from inside his six-yard box, while Jamey Osborne fired wide of the Shrimps’ goal with half-time approaching.
The home side continued on the front foot at the start of the second half with Mullin thwarted by, in turn, an offside flag, McKeown and the woodwork.
Pearson blocked a Kevin Ellison shot as the visitors failed to convert their possession into anything resembling a genuine opportunity.
Clements’ curling attempt was headed clear by Ryan Edwards, moments before Pearson hooked over Roche’s goal from Andrew’s corner.
They had two opportunities for a late leveller, the first coming on 84 minutes when the ball fell to substitute Adi Yussuf, eight yards from goal, but he was unable to get a shot away.
Then a corner found its way to the unmarked Andrew, whose shot flew inches over the angle of post and bar.
The woodwork and an offside flag then denied Bentley’s players in added time as Rhys Turner struck the inside of McKeown’s upright and Ellison’s follow-up was ruled out.
However, one goal proved enough for the Shrimps as an exhausting month comes to a close with Tuesday’s trip to Portsmouth.
Morecambe: Roche, Wakefield, Edwards, Whitmore, McGowan, Fleming, Rose, Molyneux, Evans (Wildig 70), Mullin (Turner 85), Ellison. Subs not used: Nizic, Conlan, Duckworth, Hedley, Jordan.
Grimsby Town: McKeown, Mills, Pearson, Collins, Andrew, Gunning (Davies 80), Bolarinwa (Yussuf 83), Clements, Osborne (Asante 64), Dyson, Jones. Subs not used: Disley, Boyce, Comley, Maxwell.
Referee: Darren Handley.