But the defeat means Hereford United face an uphill battle if they are to sneak into the end of season play-offs in their first season back in league football.
On a blustery afternoon, it was the visitors who created the first opening when full-back Tom Newey raced 50 yards before unleashing a powerful drive which narrowly cleared Wayne Brown's bar.
The Bulls keeper pulled off a neat save shortly afterwards when he dived to gather a low drive from Ciaran Toner.
Hereford, playing against the wind, struggled to test Phil Barnes, but the Mariners' keeper was in trouble when he flapped at a cross from Andy Williams, but Andy Ferrell's shot from the rebound deflected out for a corner.
Grimsby continued to pose the greater threat and Nick Fenton's header from a Danny Boshell cross was superbly pushed away by Brown.
Boshell's drive was then safely gathered by the United keeper, who also caught a Toner drive on the stroke of half-time.
After the break, Hereford made a lively start to proceedings and thought they had taken the lead on 54 minutes when Steve Guinan forced the ball home following a Danny Thomas cross. Referee Mark Oliver spotted an infringement, however, and disallowed the goal.
Three minutes later, it was down to Brown to save the day for Hereford again when he flew through the air to claw away Fenton's header from a Toner free-kick.
Hereford continued to have the better of the possession without being able to create real chances and they were made to pay in the 76th minute.
Substitute Peter Till's flick sent Bolland away and his shot from 15 yards flashed past the helpless Brown.
Hereford had their chances to peg the goal back, none better than three minutes from time.
Thomas again made excellent ground down the left before picking out Alan Connell, but the former Torquay striker blazed a great opportunity high over the bar and out of the ground.
In the dying seconds, Grimsby had to survive a couple of goalmouth scrambles before completing a double over the Bulls.