Jamie Devitt's 18th-minute strike kept alive Grimsby's faint hopes of League Two survival with victory at Hereford.
Midfielder Devitt latched onto a loose ball 20 yards out before rifling a shot past goalkeeper Adam Bartlett into the roof of the net.
Early in the second period Frenchman Mathieu Manset shot wide of the Grimsby post before heading a corner from Marc Pugh over the crossbar.
Just before the end Adam Bartlett made a fine save to deny Devitt a second.
Hereford director of football Graham Turner told BBC Hereford & Worcester: "It concerns me that when you are coming up against the sides in the sort of position that Grimsby are in that the players are not quite focused on the task in hand even if it is subconsciously.
"I think we had that in first 35 minutes and we were way below our capabilities in that period.
"We paid a heavy price for it and, had we been playing a side from nearer the top it changes attitudes."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.