The big striker headed over but it provided a good opening tempo to the match. It was Griffin who had another chance on 11 minutes after a good ball from Danny Senda but he failed to keep his shot down. At the other end John McDermott crossed for Jones and his far post header struck the bar on 18 minutes.
Michael Reddy was allowed through after a poor challenge by Clint Easton but keeper Iain Turner saved well with his feet on 19 minutes.
Wycombe took the lead moments later when a loose ball was put into the net by Charlie Griffin. Reddy beat Turner to the ball but Johnson was quick to clear off the line on 23 minutes.
Wycombe extended the lead on 36 when Kevin Betsy crossed from the right for Matt Bloomfield to fire home. A minute later Grimsby pulled one back when Reddy cracked a poor defensive clearance past Turner to make it 2-1 on 37 minutes.
Reddy presented plenty of problems and raced clear on 40 but Turner was out quickly to clear the danger.
At the start of the second half a cross from Senda to the far post brought a wonderful header from Bloomfield that was brilliantly saved by keeper Steve Mildenhall on 47 minutes.
On the hour a Tom Newey free kick for Grimsby from 22 yards was well saved by Turner. Bolland beat Turner to the ball but his shot was cleared before Cohen put the rebound wide on 65 minutes.
Defender Keogh sent a header goalward from a corner but Mildenhall managed to grab it. A Senda header almost got past his own goalkeeper Turner as he tried to pass the ball under pressure.
Wycombe finally took a grip when Johnson headed home a Senda free kick on 78 for 3-1.
Johnson came close to getting another when his diving header from a Senda corner flashed past the post.
Wycombe saw the game out despite a late flurry from Grimsby. This was Grimsby's first defeat on the road this season while Wycombe extended their unbeaten run to 18 matches.