Despite a big improvement from the 8-1 thumping at Hartlepool, their young side was no match for a strong experienced Swindon who took the points with a strong second half display.
Goals from skipper Andrew Gurney on 52 minutes and Tommy Mooney direct from a free kick after 64 minutes enabled Swindon to storm into a lead they did not look like letting slip.
Manager Andy King said: "Its fun watching the team at the moment. They are playing some really good stuff. Grimsby manager Paul Groves, who left himself out after the Hartlepool horror, said that Swindon were the best side he had seen this season.
He added that they were a team of men - a not so subtle reference to his young team which he is having to field at the moment because of injuries to key to experienced players.
Spirited Grimsby came out of the traps and pushed Swindon back, taking a deserved lead on 22 minutes.
Striker Jonathan Rowan, who went off injured before half time, played fellow striker Mick Boulding through and he took the ball around the keeper before rolling it in to the empty net for his sixth goal of the season.
But that was as good as it got for the Mariners and, despite throwing everything at Swindon in the closing stages, they did not have the skill to open up the visiting defence for a second time.
In fact it could have been worse for Grimsby - only an off side flag denied striker Sam Parkin a third goal.
As Swindons unbeaten run continues, Grimsby now face another home game on Saturday against bottom of the table Chesterfield and that is one they simply must win before the alarm bells ring even louder.