Max Cornhill grabbed the only goal of the game with 15 minutes to go, after Andy Cook had twice hit the woodwork for the Mariners.
Grimsby had been reduced to 10 men just before the goal after Jamal Fyfield was shown a second yellow card.
And they were unable to find a way back into the game and further enhance their play-off claims as the hosts held on to move to within a point of getting out of the Skrill Premier’s drop zone.
Town boss Paul Hurt made no less than 10 changes to his starting XI, with only keeper James McKeown keeping his place from the side that drew 2-2 with Woking 48 hours ago.
He lined up behind a defence of Paul Walker, Chris Doig, Clayton McDonald and Fyfield.
Joe Cobeck, Andi Thanoj, Paddy McLaughlin and Ross Hannah made up the midfield quartet, with Oumare Tounkara and Cook starting in attack.
The Grimsby bench had a very youthful look to it, with Caine Winfarrah, Dayle Southwell, Ellis Humble and Tom Charlesworth alongside reserve goalkeeper Jonathan Hedge.
Town had the first real chance of the game when a shot from Hannah was saved by home keeper Alan Julian and Cook could only send the rebound over the bar.
Another attempt from Hannah came on six minutes but this time, he did not force Julian into action.
Danny Harris looked to create an opening at the other end on eight minutes but Walker did well to halt his progress and the striker was unable to find team-mate Cornhill.
A free kick from Lee Noble caused problems in the Town defence before the visitors cleared and launched a counter-attack, although Lee Burns got back to deny Hannah.
Thanoj was the first to be shown a yellow card for a foul on Jim Stevenson but the resulting free kick did not lead to a goalscoring opportunity.
A Dartford corner was then headed away by Tounkara, before the return ball into the Town box was claimed by McKeown.
The Mariners then went close to opening the scoring on 19 minutes when Cook took the ball and struck a shot from 25 yards that beat Julian but bounced down off the underside of the bar and did not cross the line.
Ben Swallow then hit a shot for the hosts but it caused no problems for McKeown, who was able to watch the ball go well wide of his goal.
A Town corner came just after the half-hour but the delivery beat everybody and Dartford broke, with a move that ended when striker Mikel Suarez failed to connect with a shot.
Another corner came when Cook found Colbeck but defender Rory McAuley got there first when he tried to return the ball to the big striker. Again, nobody could connect with the ball from the flag.
Noble hit a cross from the left for the home side soon afterwards and after it was touched on, McKeown had to dive to his left to make the save.
Cook sent a header straight at Julian after a cross from Hannah, before a centre at the other end was cleared from danger by Walker.
A Dartford corner then presented an opportunity for the home side when the delivery was met by Cornhill but he could only head wide.
Town’s next attack led to Tounkara hitting a shot on the turn which narrowly missed the target, before Suarez headed over the bar at the other end as both teams looked for the opening goal.
One added minute was played at the end of the half and with no further chances for either side, the game remained goalless at the break.
No changes were made before the restart and Town’s first attempt of the second half came four minutes in, when Cook laid the ball off for Colbeck but his powerful shot missed the target.
Dartford won a corner three minutes later but the corner was headed over by Suarez after Danny Harris had won the initial flick-on.
Fyfield was booked for a foul on Swallow, before Tounkara got to a long ball from McKeown ahead of Julian but the ball went out for a goal kick.
Another cross from the home side was cleared by Walker, before a shot from Noble deflected off McDonald but McKeown got down to prevent the corner.
Town went close to taking the lead on 63 minutes and again, it was Cook who was inches away from scoring. The striker rose to meet a Thanoj free kick but his header bounced back off the post.
Southwell replaced Tounkara as the Mariners made the first substitution with 25 minutes to go, with the sub taking up a position on the left as Hannah moved alongside Cook up front.
Neither side was causing the opposition defence any major problems as the midway point of the second half passed.
The home side changed that with a little less than 20 minutes to go though, when a free kick was met by Cornhill but McKeown managed to get fingertips to the ball and stop it going into the bottom corner of the net.
Dartford were given a numerical advantage soon afterwards when Town were reduced to 10 men as Fyfield picked up a second booking for a foul on Noble.
And they were ahead on the scoreboard too soon afterwards, when a corner was met by CORNHILL and his header beat McKeown to make it 1-0 with 15 minutes to go. The Town keeper was shown a yellow card for protesting after the goal was given.
Winfarrah replaced Hannah and took up a left-back position to cover for Fyfield for the remainder of the game.
Grimsby were struggling to make an impression in front of goal and were now running out of time to get anything from the game.
Doig was the next to be shown a yellow card for a foul and despite four minutes of added time being played, Town were unable to find an equaliser.
The Mariners are next in action on Saturday, when Chester are the visitors to Blundell Park.