But a last-gasp goal from Lenell John-Lewis gave them a lifeline and ensured they still have a fighting chance of a return to Wembley.
The Mariners were second best in the first leg of their semi-final at the Abbey Stadium and the Us will bring a 2-1 advantage to Blundell Park for next week’s return fixture.
Striker Ryan Bird put the home side ahead on 20 minutes, before doubling the Cambridge lead after half-time.
Town rarely threatened but they struck at the death to put a completely different complexion on the tie and set things up nicely for the second leg.
Four changes were made to the Town side after the goalless draw with Southport last time out.
Sam Hatton replaced Paul Bignot at right-back and Chris Doig was the man to come in for the suspended Shaun Pearson in the centre of the back four, while Paddy McLaughlin was preferred to Scott Neilson on the left wing and Andy Cook was given the nod up front as Ross Hannah dropped to the bench.
James McKeown started in goal, with Hatton, Doig, Clayton McDonald and Jamal Fyfield forming the defence.
Alex Rodman began on the right of midfield, with Craig Disley and Scott Kerr in the middle and McLaughlin on the left. John-Lewis partnered Cook in attack.
The Town substitutes were Andi Thanoj, Neilson, Hannah, Aswad Thomas and Oumare Tounkara.
Cambridge went into the game without former Grimsby centre-back Ian Miller, who was out injured.
Harrison Dunk was another absentee because of injury, while Matthew Barnes-Homer missed out through being cup-tied.
Town kicked off with a strong wind at their backs and immediately, McLaughlin tried a shot from inside his own half which narrowly cleared the crossbar.
At the other end, McDonald had to head over his own bar to concede the game’s first corner with less than two minutes on the clock.
Another corner came soon afterwards and Kerr cleared after Fyfield was beaten in the air. Cambridge worked the ball back and McKeown was called into action for the first time to make a save from Ryan Donaldson.
Another shot, this time from Ryan Bird, was blocked after play was allowed to continue following a handball appeal against McDonald in his own penalty area.
McDonald was shown the first yellow card of the afternoon for a foul on striker Tom Elliott on 12 minutes but the resulting free kick did not cause any problems as it was dealt with by Doig.
The home side had made the better start to the game and they took the lead on 20 minutes, when the ball was played by Andy Pugh to BIRD and he drilled a shot past McKeown from just inside the penalty area.
McDonald had to concede another corner two minutes later after a cross from Kevin Roberts but the Mariners were able to deal with the danger and get the ball away after Bird failed to connect with the low delivery.
Town struggled to make an impression in front of goal during the first quarter of the game but they had an opportunity on 26 minutes, when a Hatton cross was headed over the bar by John-Lewis.
Cambridge were creating better chances and they could have stretched their lead when a cross came in from Roberts but midfielder Luke Berry could not get enough power on his diving header and the ball rolled just past the far post.
Rodman had to clear after a blocked shot looked to be heading into the path of Donaldson as the hosts continued to threaten after the half-hour mark.
A spell of Town possession came 10 minutes before the break but it did not lead to a chance in front of goal, as Hatton’s through-ball proved to be too far ahead of Disley.
A floated free kick from Hatton was headed away for a Town corner two minutes later but from the low delivery, Cambridge broke through Donaldson, although he was eventually crowded out.
Another home corner came as half-time approached but again, it was dealt with by the Grimsby defence.
One added minute was played at the end of the first half and a McLaughlin cross was taken by home keeper Will Norris.
That proved to be the last opportunity of a first half which had belonged to the home side, although the Mariners were only one goal down and therefore still in the game.
No changes were made at the interval and a second Cambridge penalty appeal came when Bird went down inside the box under a challenge from Fyfield, although the referee ruled it was a fair one and the game continued.
Donaldson volleyed over the bar four minutes in after McKeown failed to fully deal with a high cross, as the hosts continued to attack.
Town won a corner on 53 minutes but it was cleared, although Fyfield retrieved possession and crossed from the left. Again though, the ball was headed away from danger by defender Liam Hughes.
The Mariners had made a better start to the second half but they were to fall further behind when Greg Taylor was given space to cross for BIRD to head home unchallenged and make it 2-0.
John-Lewis missed the target with a shot as the visitors looked for a response, with Town now facing an uphill struggle to get themselves back into the game and keep the tie alive.
Tom Elliott got past Doig and sent a cross in which nobody could connect with as Cambridge looked for the third goal which could possibly all but kill off the tie.
Bird was continuing to be the main danger man for the hosts, volleying over, then seeing a shot blocked by Doig as he chased his hat-trick.
A foul on John-Lewis gave Town a free kick just outside the Cambridge box on 68 minutes but Hatton’s shot went into the home wall. The referee spotted encroachment by Berry though and after he was booked, Hatton was given a second chance with the set-piece. The result was the same though as his shot hit the wall.
Kerr was replaced by Neilson as Paul Hurst made the first substitution of the game soon afterwards, meaning McLaughlin moved inside as the sub took up a position on the left wing.
A shot by Rodman was deflected behind for a Grimsby corner but the delivery was poor and Cambridge broke quickly, with Hatton having to get back well to deny Berry.
Cook was caught offside as he looked to get to a pass from John-Lewis, before the former Barrow striker was replaced by Tounkara for the final 15 minutes of the game.
Richard Tait came on for Pugh in the home side’s first substitution three minutes later, while Thanoj replaced McLaughlin as Hurst made his third and final change.
John-Lewis had Grimsby’s first shot on target with 11 minutes of the game to go but it was comfortable for keeper Norris.
A Town corner with nine minutes to go was half-cleared, before Neilson sent a cross straight to Norris.
Neilson cleared the crossbar with a shot soon afterwards as the Mariners looked to make their task in the second leg slightly less difficult by grabbing a late goal.
Instead, it could have got worse, as McKeown was forced to make a good save from Berry with five minutes to go.
The travelling Town supporters appealed for a penalty after Tounkara went down inside the box on 88 minutes but the referee waved play on.
Four added minutes were signalled by the fourth official, giving the away side more time to try and snatch a goal that would halve their deficit.
And with the last action of the game, they had their lifeline, as a corner fell for JOHN-LEWIS and his header sneaked inside the post to make it 2-1.
With the first-leg advantage, Cambridge will be favourites to book their place in the final.
But at 2-1, the Mariners are definitely still in the tie and will feel they can complete the comeback in the second leg at Blundell Park next Saturday.
Before that, Town are in action on Tuesday, when they travel to Barnet in the league.