The experienced targetman's goal was his first in the EFL for the Sulphurites and sealed a fourth triumph in five home outings for a team who had struggled for victories on home soil until the turn of the year.
And, another three points lifts Simon Weaver's team up to 12th in the League Two standings; five points shy of the play-offs and 16 clear of the drop-zone.
Fighting for their lives at the wrong end of the table, visiting Grimsby lined up with three centre-halves and operated with a back-five when out of possession, making their intentions clear from the first whistle.
Their tactics presented Harrogate with plenty of space in the midfield to play in, and they utilised it well enough, producing some tidy spells of football on a difficult surface.
The opening 45 was virtually one-way traffic, the Lincolnshire outfit struggling to escape their own terrirory but surviving courtesy of some proactive goalkeeping from Sheffield United loanee Jake Eastwood and, on occasion, thanks to the sheer number of bodies inside their penalty area.
George Thomson tested the visiting custodian with a well-struck long-range drive on 10 minutes before Eastwood produced a superb parry to keep out Josh March's stinting volley.
Simon Power's cross from the right then dropped on top of the Mariners' cross-bar, while Eastwood was again pressed into action shortly before the interval when Aaron Martin directed a header from another Power delivery towards the bottom corner.
Some desperate defending inside their own box kept the away side on terms as Town continued to press, but with 41 minutes on the clock, Paul Hurst's men almost snatched the lead despite having offered nothing as an attacking force up to this point.
Thomson was caught in possession inside his own half, allowing Idris El Mizouni to send Payne in on the home goal down the left, though the powerful frontman was thwarted by a good James Belshaw stop.
Town continued to press right up until the interval, and although they remained in the ascendancy during the early stages of the second period, the game began to drift.
With Martin looking tired up front, the ball was no longer sticking in the final third and Grimsby started to grow into the contest.
After James Hanson's 68th-minute header extended Belshaw, Weaver rightly opted to freshen things up with a triple-substitution.
And it was one of those players who entered the fray that made the difference, Beck getting across marker Luke Waterfall to guide a clever header from Ryan Fallowfield's right-wing centre inside the far post on 77 minutes.
Buoyed by their goal, Town looked to try and kill the game off, though the closing stages saw the Mariners have a real go at getting back into the contest and Hanson fired over a gaping net with an instinctive first-time strike after Belshaw's awkward punch landed at his feet.
Filipe Morais then saw a blast deflected over the cross-bar and, in the very last seconds of stoppage-time, Joe Adams got free at the back post after a long diagonal from the right caught Town out, though his effort was half-charged down and spun into the grateful arms of Harrogate's number one.
Harrogate Town: Belshaw; Fallowfield, Smith, Hall, Jones (Burrell 69); Power, Thomson, Kerry (Falkingham 81), McPake; March (Muldoon 69), Martin (Beck 69). Unused substitutes: Minter, Francis.
Grimsby Town: Eastwood; Hewitt, Pollock (Adams 80), Waterfall, Menayese, Hendrie; El Mizouni, Coke, Matete (Morais,79); Hanson, Payne (John-Lewis 69). Unused substitutes: McKeown, Rose, Green, Habergham.
Referee: T Kettle (Rutland).