It was hardly classic stuff from the Mariners but Chester seldom managed to threaten and, had Grimsby not missed a late penalty, the score line would have been more convincing.
Chester in fact only threatened twice in the first minute of each half with Stuart Drummond heading wide up from a corner and top scorer Ryan Lowe shooting into the side net with the second half just underway.
To be fair Grimsby seldom managed much of a threat either in a tedious match and the one goal proved just enough to win the points.
It came four minutes from half time after good interplay between midfielder Curtis Woodhouse and skipper John McDermott. Woodhouse crossed from the right and Gary Jones lost his man to dispatch a header beyond the Chester keeper for his seventh goal of the season.
Grimsby might have had a second with the last touch of the first half, but a header from central defender Ben Futcher was blocked on the line by keeper Stephane Gillet.
The second half barely improved, although the game could have got out of hand following an incident between Chester defender Carl Regan and Grimsby striker Gary Cohen. Amazingly the referee took no action and it all got a little fractious after that.
Grimsby were provided with the perfect opportunity to settle the nerves with just seven minutes left.
But Drummond clearly pushed Woodhouse in the penalty area and the midfielder got up but continued Grimsby's appalling record from the penalty spot when he blazed high, wide and not very handsome.
After that Chester sensed that there might be a point up for grabs and there were four minutes added time, but Grimsby held on for a precious victory.
With the three teams at the top all winning Grimsby had to get the three points to maintain third place, while Chester have now lost 12 of their last 13 league games.