Jarman's third goal of the season presented Grimsby with some much needed breathing space at the wrong end of the table with their first win of 2009.
The Mariners were certainly worth the three points and although Wycombe had opportunities to respond, they had very few shots on target.
Jean-Louis Akpa-Akpro had the first chance of the game for Grimsby but volleyed wide on four minutes.
Stuart Elliott also had a free-kick go wide on 12 minutes, but Jarman made no mistake on 24 when he latched onto Akpa-Akpro's right-wing ball.
Akpa-Akpro received the ball from a long punt forward from his goalkeeper Phil Barnes before whipping a cross in to Jarman, who slammed it past Scott Shearer from close range.
Matt Bloomfield almost responded for the hosts two minutes later but headed wide from a corner.
Matt Harrold also glanced a header wide five minutes before the break as Wycombe began to build some pressure.
Harrold and Jarman both squandered chances for either side early in the second half, while Adam Proudlock had a shot cleared off the line by Gary Holt.
Three minutes before the hour, Scott McGleish was played in by Chris Zebroski but fired wide for the hosts from just six yards out.
Sub Angelo Balanta shot wide as the hosts became frustrated later in the half, while Elliott saw his 25 yard fizzer fumbled by Shearer.