It was a far cry from their last win, the famous 1-0 victory over Football League side Exeter City in front of the BBC cameras back in 2014, and they survived a real scare against a team three tiers below them in the football pyramid.
Aboubacar Sanogo’s header off Sean Williams’ corner 11 minutes from the end proved enough to send the Yellows through to the second qualifying round, the draw for which will be made on Monday.
Paul Carden paid the upmost respect to the opponents by naming a virtual full strength side, the only change from Monday’s win at Marine saw Joe Mwasile come in to the starting line-up for Josh Hine, with reserves forward Dylan Glass stepping up to the bench.
The game started slowly and the visitors visibly grew in confidence as the first half went on.
While the Yellows dominated possession, they couldn’t break down a Borough team that was superbly marshalled at the back by Josh Sunter.
The best chance of the half fell to Tony Gray, who hit the crossbar, but was otherwise left frustrated by a lack of service.
Grimsby felt they should have had a penalty six minutes before the break when Jack Bradbury went down awkwardly in the box under the challenge of Tony McMillan, who had clearly taken the ball in doing so.
As has been the case in recent weeks, the Yellows came out after the break in much more spritely fashion and they hit the woodwork again within two minutes of the restart, Gray’s stretched header knocking back Liam Goulding’s right wing cross.
Goulding himself had a chance on the hour mark, turning well on to Sean Williams’ delivery and then having his shot saved by Scott Drury’s legs.
But again, the visitors were encouraged by the hosts frustrations and while they didn’t create anything of great alarm, Jack Debnam did warm the palms of McMillan with a shot from the edge.
As time ticked by, and the hosts wondered whether a replay might be needed, they finally broke the deadlock.
Williams’ floated corner was powered home by the head of substitute Sanogo.
That proved enough, and Warrington will now travel to Workington for their league fixture on Tuesday, looking to maintain their berth at the top of the Evo-Stik Premier League.
Warrington Town: McMillan, Goulding, McKeown, Richards, McCarten, Baker, Mwasile (Kinsella), Williams, Gray, Vassallo (Glass), Hughes (Sanogo). Unused subs: Carden, Ascroft.
Grimsby Borough: S Drury, A Drury, Briggs, Smythe (Steel), Sunter, Peers, Rowbotham (Ashton), Venney, Trott, Debnam, Bradbury (Wroot). Unused subs: Moody, Barrett, Petronzio.