But, after taking an early lead, they were almost undone in the final seconds when a tremendous save from keeper Willy Gueret denied central defender Nick Fenton and then substitute Martin Butler headed wide from an open goal three minutes into added time.
But overall it was a well deserved victory for the Dons who took an early lead following a corner from Colin Cameron on nine minutes.
Cameron, who ran things in midfield, floated over a cross which was met by the head of skipper Sean O'Hanlon and his header found the net despite a desperate attempt to clear from home defender Rob Atkinson.
The Dons bossed the remainder of the first half as Grimsby struggled to create much. Peter Till and Peter Bore up front were unable to forge anything like a strike partnership.
In fact it took a fine save from Mariners keeper Phil Barnes to deny John Miles just before half-time.
It was a different story in the second half with Butler and Gary Jones replacing Till and Bore as Grimsby started to dominate for the first time in the game.
But this eventually petered out and it was the Dons who got back on top without seriously threatening to add to their lead.
And they were nearly caught out twice late on before chalking up yet another victory on their travels.
So the dress rehearsal for the Johnstone's Paint Trophy Final in just over three weeks went the Dons' way, but Grimsby showed enough to make it clear it won't be one-way traffic at Wembley, although the League Two leaders will be strong favourites.