But the visitors had to withstand a late Orient bombardment as Efe Echanomi pulled a goal back nine minutes from time and the home side had a couple of stoppage time chances to level things up.
In a frantic finish Orient loan signing Scott Fitzgerald and Grimsby's Ronnie Bull were dismissed by referee Steve Tanner.
However, it would have been rough justice on Grimsby had Orient snatched a point at the death.
The visitors were well worth the victory and showed their intentions when they rattled the Orient bar after just six minutes when giant defender Robert Jones soared high above the defence.
Orient responded briefly and Fitzgerald fired over and then Lee Steele was denied by Town goalkeeper Anthony Williams.
But Orient were cut apart on 19 minutes when Michael Reddy's excellent run down the right set up Parkinson for the easiest of finishes.
Things almost got worse for Orient as goalkeeper Lee Harrison was forced to pull of a smart stop just before the break to deny dangerman Gritton.
In the second half Orient threatened to take control but Grimsby were always dangerous on the counter attack and Harrison had to be at his best to keep out another Jones header.
The visitors grabbed a second when Reddy set up Gritton who squeezed the ball into the net at the far post.
Two minutes later Parkinson should have had a third when he raced clean through but was denied by the alert Harrison.
Orient threw caution to the wind in the final 15 minutes as defender John Mackie was pushed up front and it was his header from a Michael Simpson free-kick that led to Echanomi scoring at the far post.