United created chances from the off and nearly took the lead in the second minute when Rob Kozluk's cross was only just headed over by Asaba.
Next it was Grimsby's turn, Coyne's goal kick eventually found ex-Barnsley midfielder Darren Barnard but his 20 yard effort failed to find the goal.
Another chance arose for United a minute later but again Carl Asaba failed to find a route to goal. Grimsby went straight up field on attack but John McDermott's shot was foiled by Blades keeper Paddy Kenny.
In the eighth minute Kenny was found picking ball out of the net. Stuart Campbell beat off Rob Ullathorne on right-wing and his low cross was met by the boot of Paul Robinson who was more than happy to score his first goal for the Mariners.
Welsh International, Darren Barnard attempted to put Grimsby 2-0 up but his long range shot in 18th minute curled wide of Kenny's post.
Asaba had a fantastic opportunity to draw level when Peschisolido put Carl through but Coyne's World Class save stopped him from doing so.
Just before half-time Paul Peschisolido (twice) and Stuart McCall both shot at goal but again Coyne's fine goalkeeping stopped United from scoring.
Half-Time: Sheffield United 0-1 Grimsby Town
United created few chances with the best coming from Michael Tonge who put his shot over the bar.
Just after the hour mark Neil Warnock seriously changed the team when he took off United's front men Carl Asaba and Paul Peschisolido for Peter Ndlovu and Laurens Ten Heuvel.
United did not get much better but improved slightly, Ndlovu and McGovern both went close before Warnock made his final change. He took off Jon-Paul McGovern and put on Wayne Allison, changing to the 4-3-3 formation in 78 minute.
Allison was not on pitch for long when his first chance came along on 83rd minute, McCall's cross met Wayne's head but Coyne's brilliant save forced a corner on the left hand side. The corner, taken by McCall was cleared for another corner but on right hand side.
Stuart McCall delivered the cross from the right, Wayne Allison rose higher than anyone else on back post and to to relief of Blades fans headed home into far corner, in front of the Hallam FM Kop.
Now United had equalised it looked as though it would stay at 1-1 but o no, it was in the script that United would win this game.
United got that goal in the last minute, Kenny's long kick upfront went straight over Allison's head, Laurens Ten Heuvel beautifully chipped the ball over Mariners defenders and their was young Michael Tonge to volley the ball home.
After 89 minutes of time wasting Grimsby decided that time wasting was no longer a option but the Blades were too sharp for Grimsby and all three points went to United.
Full-Time: Sheffield United 2-1 Grimsby Town
Verdict: In the eyes of a Blades fan I think its fair to say that Town gave a better performance than United and really should have won. However credit is due to Neil Warnock who threw Wayne Allison right in the deep who, thankfully came up trumps.
MOTM: The man of the match award v Grimsby Town will go to Wayne Allison, though on pitch for only 13 minutes he won every ball in the air when we had been struggling to do so all match, and also he scored a brilliant goal to cap it all off.
For the first time this season I have decided to award opposition their man of the match. On loan sticker Steve Kabba had a brilliant game for the Mariners (he reminded me of Emile Heskey with the way he plays), he ran the United defence all over place.