Although they only scored the one goal they might have had more - a fact acknowledged by manager Martin Ling.
There was, however, some controversy with the goal as the ball appeared to go out for an Orient throw and, when Justin Miller crossed from the right, Craig Easton burst through to head strongly into the net.
The goal came in the final minute of the first half and gave Orient an advantage which they rarely looked like squandering.
Grimsby had been ineffective up front in the first half with Michael Reddy playing despite not being well and fellow striker Gary Jones out of touch.
It was inevitable that manager Russell Slade would make changes early in the 2nd half and with less than 10 minutes on the clock he sent on Martin Gritton and Gary Cohen in a double switch.
It was Gritton who wasted Grimsby's only real chance of the game when he broke into the box and indecision cost him dear with his weak effort trickling past the post.
By then Orient could have had the game sewn up when skipper Gary Alexander going for a record 10th game with a goal was denied by a great save by a former team-mate in Steve Mildenhall in the Grimsby goal.
But clear-cut chances were few and far between and on a greasy surface control was difficult.
The game's outstanding player was Orient striker Jabo Ibehre, who was a handful for the Grimsby defence all afternoon, and they must have been relieved when he was taken off injured with over 20 minutes to go.
Grimsby pushed more and more men forward but the Orient defence was untroubled and keeper Glyn Garner did not have a serious save to make all afternoon.