One change was made to the Town side that drew with AFC Telford United last time out, as Aswad Thomas returned from injury and replaced Toto Nsiala in the starting XI.
That change saw Carl Magnay go back to his usual right-back position, as Thomas slotted in on the left and Daniel Parslow moved inside to partner Shaun Pearson at centre-back, in front of goalkeeper James McKeown.
The midfielders were Jack Mackreth, Craig Disley, Scott Brown and Nathan Arnold, with Lenell John-Lewis and Pittman again selected in attack.
There was also one change on the Grimsby bench, as Rotherham loanee Nicky Walker replaced Hamish Watson. The other substitutes were Paul Bignot, Ross Hannah, Scott Neilson and Craig Clay.
The game kicked off after a 75-minute delay caused by the Town bus getting caught in traffic on the way to the West Midlands.
The Mariners had the first chance within 30 seconds, when Pittman hit the bar after cutting in from the right as keeper Christian Dibble was left stranded.
The hosts won the first corner of the game on two minutes but Town managed to clear their lines through Brown and Pittman.
John-Lewis had a double chance on 10 minutes but his first effort was saved after a cross from Arnold and then he shot wide after the ball was worked back to him.
A cross from Adam Dawson was blocked at the other end, before a Town attack ended when Mackreth was adjudged to have run the ball out of play for a goal kick after a ball over the top from Brown.
Striker Onome Sodje hit a shot well over the bar for the hosts on 20 minutes after Disley had first lost possession and then done well to get back and put a challenge in.
A Mackreth cross was comfortably claimed by Dibble four minutes later after a spell of Grimsby possession.
And the Town pressure told soon afterwards, when they took the lead. A low ball from Magnay found PITTMAN on the edge of the box and he turned before firing it past the keeper.
Another Town attack saw an Arnold cross headed away before Disley could get to it, before a follow-up ball from Brown was also cleared.
Brown missed the target with a shot from 20 yards on the half-hour as Town continued to do most of the attacking.
Town won a free kick in the Nuneaton half five minutes before the break and after it was played short for Arnold, the ball was worked to Thomas and his cross was headed over the bar by Pearson.
One added minute was signaled as another Grimsby free kick was awarded, level with the penalty area. Arnold’s delivery was headed out for a throw-in.
That proved to be the last chance of a half which was dominated by the visitors, who were comfortable at the break, albeit with only a one-goal advantage.
No changes were made before the restart and after a Nuneaton corner was cleared, the Mariners had a chance from the flag at the other end but Magnay headed over the bar.
A concern for manager Hurst was Disley hobbling out of play to be replaced by Craig Clay, just as Arnold kept the pressure on with a thumping 25-yard shot that rocked the stanchion behind the goal.
Instead it was to get worse for the hosts as Gareth Dean dragged down the onrushing John-Lewis in the final third. The Nuneaton defender was the last man and had to walk but from the resulting free kick the game would take an even more dramatic twist, Dibble did well to keep out Thomas' set piece, colliding with the post in the process. That forced the goalkeeper off and with no substitute stopper, midfielder James Armson had to don the gloves.
And Town took full advantage of that, John-Lewis testing the woodwork again with a 20-yard effort before the former Bury man placed a shot wide when played in by Pittman.
But the second goal did arrive with 15 minutes on the clock. Pittman was again involved, picking out the run of MACKRETH, and he calmly side-stepped Armson before rolling into the empty net.
Ross Hannah and new loan signing Nicky Walker were given a run-out for the final ten minutes as the Mariners eased to victory.
The home side's only real effort of note came with four minutes left of the game as Thomas hacked off his own goal-line after a shot from Anton Brown sneaked through a crowd of players.