They missed some great chances to add to Delroy Facey's 37th-minute match-winner which came following a fine run by the speedy Myles Weston.
Although Facey looked offside when he turned the ball in from almost on the goal-line, Grimsby boss Mike Newell refused to blame this decision for his side's defeat.
With only one home win all season and just a couple of victories to their name all told, Grimsby were sluggish and only during the first ten minutes of the second half and the last five minutes plus added time did they seriously threaten to unlock a splendid Notts defence.
But the visitors could have avoided all this uncertainty if they had taken their chances with Facey and fellow striker Sean Canham the main offenders.
And although manager Ian McParland was delighted to pick up an away win he is more concerned in turning round their disappointing home form.
They have a tough-looking home clash with Rotherham on Sunday where he is hoping his side will turn on a show and in turn pick up three much-needed points at Meadow Lane.
Grimsby for their part must travel over the Pennines to Accrington where their last two visits have ended in embarrassing 4-1 defeats and boss Newell has stressed the importance of picking up something this time.