The Mariners looked the better side for much of the first half and they took the lead through Scott Neilson.
But their visitors were back in the game before the interval, when a cross by Jonny Hunt was deflected into his own net by Shaun Pearson.
Town pressed for a winner throughout the second half as Wrexham caused few problems but for long periods, it looked like they might be forced to settle for a third consecutive 1-1 draw.
But Disley’s goal and a third from Andy Cook in stoppage time meant it was a return to winning ways and an important three points in their play-off bid.
Connor Jennings came back into the Town starting XI after traffic problems saw him named as a substitute for Tuesday’s draw against Hereford.
He was preferred to Ross Hannah, who scored the Mariners’ goal in that game, while Sam Hatton and Neilson also came into the line-up as a total of three changes were made.
James McKeown started in goal, with Hatton slotting in at right-back in place of Paul Bignot and Pearson, Andrew Boyce and Aswad Thomas making up the back four.
Alex Rodman began on the right side of midfield, with Disley and Andi Thanoj in the centre as Scott Kerr made way for Neilson, who started on the left.
Lenell John-Lewis joined Jennings in attack, while Kerr, Bignot, Hannah, Cook and Paddy McLaughlin were all on the bench.
Wrexham had endured a disappointing campaign so far and sat 10 points adrift of the play-off positions at kick-off but would still have slim hopes of catching the teams involved in the fight for promotion.
Rob Ogleby and Joe Anyinsah were the strikers charged with firing the Red Dragons to victory, while veteran forward Brett Ormerod was named on the bench.
Town kicked off attacking the Pontoon Stand end and their first chance came inside the opening two minutes, when a long ball from Boyce picked out Jennings but his flicked shot was blocked by visiting keeper Andy Coughlan.
The hosts retained possession and the ball was sent back into the danger zone but Disley headed wide.
A shot from Anyinsah was held by McKeown as Wrexham threatened for the first time, before Grimsby perhaps should have taken the lead when Rodman squared for John-Lewis inside the penalty area but the striker could only side-foot over the bar.
Jennings was fouled to give Town a free kick on the left on eight minutes and Hatton’s low delivery went through to Coughlan, who got down well to make the stop.
Wrexham were yet to pose much of an attacking threat at the quarter-hour, although a cross from the right almost fell for Ogleby but McKeown stretched out to claim the ball at the second attempt.
A volley from captain Dean Keates cleared the bar as the visitors began to come into the game, while Grimsby had started brightly but were now struggling to keep possession for long enough to build up attacks.
Anyinsah scuffed a shot wide after making his way into the penalty area on 20 minutes, before Town’s next attack saw them open the scoring. John-Lewis held the ball up for NEILSON, who advanced into the box before applying a calm finish to beat Coughlan and find the bottom corner of the net.
Another chance came on 24 minutes and again, John-Lewis was involved from the start. He found Thomas on the left, who played a one-two with Neilson before crossing for John-Lewis to shoot wide.
A long kick forward by Coughlan was met by midfielder Mark Carrington two minutes later but his header was off-target.
Another opportunity came for the visitors when Disley gave the ball away in midfield and Anyinsah and Ogleby broke. Pearson got back well though to put a challenge in, before Boyce completed the clearance.
A long throw from Hatton was headed behind for Grimsby’s first corner of the game 10 minutes before the break and after Thanoj’s kick was half-cleared, Boyce returned the ball into the box and eventually, a shot from Rodman was blocked.
John-Lewis then battled well to win the ball in midfield two minutes later and he advanced before playing it to Rodman, who again saw his shot blocked from the edge of the area.
Town had been the better side for most of the half but they were pegged back two minutes before the break, as Hunt beat the offside trap and his cross hit PEARSON and deflected past McKeown for an own goal
At the other end, a low cross from Thomas proved to be too close to Coughlan, who claimed the ball.
Two added minutes were signalled by the fourth official and Rodman narrowly failed to connect with another Thomas cross from the left at the far post.
The final chance of the half came when Jennings was fouled 25 yards from goal but Hatton’s free kick was pushed away by Coughlan after the ball bounced awkwardly in front of him.
That meant the scores remained level at the interval, although the Mariners would have been disappointed not to be going in with the lead.
Both teams were unchanged at the restart and an early free kick taken by Hatton from the halfway line was well claimed by Coughlan.
A trip by Disley gave Wrexham a free kick in a similar position seven minutes in but Boyce headed it clear.
Rodman won a corner on the right soon afterwards and Thanoj’s delivery picked out Pearson on the penalty spot. His downward header was dealt with by Coughlan, who gathered it at the second attempt as Jennings looked to pounce on the rebound.
A deflected shot by Rodman was pushed away by the keeper on 56 minutes, before John-Lewis failed to take advantage of the loose ball.
Wrexham won a corner two minutes later but Carrington’s delivery beat everybody and went out for a Town throw.
Ormerod replaced Anyinsah as the visitors made the first substitution of the game just before the hour.
Town’s next attack saw Rodman go on a solo run down the right before cutting in and firing a shot which was deflected wide for a goal kick.
The right winger was then involved again soon afterwards, when his cross was headed over the bar by Thanoj.
A Grimsby corner from the right was cleared but they won a throw-in and worked the ball back to win another corner, which was also dealt with by the Welsh side.
Neat play by Jennings and John-Lewis down the middle looked like it had led to a chance for Neilson but the offside flag went up as the ball was pushed through to the winger.
Town looked to have created another good opportunity with a quick break through Jennings and Rodman but John-Lewis was crowded out as he looked to shoot, before Thannoj headed over the bar from a Rodman cross.
Cook came on for John-Lewis with 19 minutes to go and he almost had a chance to put his side ahead when he looked to turn a good pass from Hatton towards goal butt defender Danny Livesey did well to block the effort for a corner.
Town were doing most of the attacking as they pushed for a winning goal and a corner from the left eventually led to Cook missing the target with a far-post header.
Midfielder Jay Harris replaced striker Ogleby for Wrexham with nine minutes to play, suggesting the away side may have been looking to settle for one point.
Ormerod, now playing up front on his own, was booked for kicking the ball away before a Town free kick, which ended with Cook heading wide after a long ball forward from McKeown.
Hannah came on for Jennings for the last five minutes, with Grimsby still looking for a winning goal.
And that goal came with three minutes left, as a looping cross from Thomas on the left was met by DISLEY, who headed it back across goal and into the net to give the hosts a precious advantage.
McLaughlin came on for Neilson for the closing stages of the game as Town looked to see out the game and claim the three points.
And their victory was sealed in stoppage time, when good persistence from COOK saw him get into the penalty area and beat Coughlan to make it 3-1.
The Mariners are next in action when they travel to Forest Green Rovers on Tuesday.