There was just one goal in it but Wycombe were much better than their mid-table opponents, who had little to offer but spirit.
Grimsby went close in the third minute when a shot from striker Martin Butler was deflected wide, but otherwise keeper Frank Fielding had little to do.
Wycombe gradually got into the game and it was no surprise when they took a 19th minute lead.
Striker Delroy Facey had already looked good and he played a pass for Argentinian midfielder Sergio Torres to burst into the box and beat keeper Phil Barnes with a low shot.
Wycombe could and should have had more goals before half-time, but at 1-0 down the home side were still in it.
Grimsby had been forced to re-shuffle when dominant centre-back Nick Fenton limped off injured and they brought on a couple of subs as the second half wore on.
But as Wycombe stepped up the pressure, they could have increased their lead on a couple of occasions.
Firstly, leading scorer Scott McGleish was sent clear but his shot was blocked by the legs of Barnes and then midfielder Stefan Oakes hit the outside of the post from 30 yards when the keeper cleared the ball out of his hands.
Grimsby were then indebted to midfielder Paul Bolland for clearing off the line as Wycombe sought the second goal that would have put the game beyond doubt.