The result was never in doubt after Lincoln skipper Paul Morgan's header set up Forrester in the 43rd minute.
The former Grimsby player swivelled inside the six-yard box before firing past keeper Phil Barnes.
Lincoln dominated the rest of the game and added a second goal but could have easily have won by a much bigger margin.
Grimsby's only real chance came early in the game when Martin Paterson charged down a clearance from Nat Brown. The ball ran kindly for Isaiah Rankin but the striker's shot was blocked at point-blank range by Lincoln keeper Alan Marriott.
Forrester's goal broke the deadlock and almost immediately the striker threatened again only to be brought down by Gary Jones on the edge of the box. Jones was yellow-carded and then Barnes produced a superb one-handed save to keep out the free-kick from Shane Nicholson.
From the resulting corner, Lincoln's Lee Beevers produced a powerful header which was blocked on the line.
In the 57th minute Morgan was denied by another goal-line clearance. Grimsby responded by pulling off Peter Bore and moving Jones up front.
But Jones only lasted nine minutes in his new role before earning a straight red card from referee Mike Riley for elbowing Brown off the ball.
Lincoln clinched the game in the 73rd minute when a long throw from Nicky Eaden was headed on by Martin Gritton. Midfielder Lee Frecklington was first to react and hit a rising shot into the roof of the net to give Barnes no chance.
Frecklington went close again four minutes later with a left-foot shot from the edge of the box, which flew inches over the bar.
Grimsby could hardly string two passes together and their supporters streamed away from the ground ten minutes from time.
Lincoln almost scored a third goal in stoppage time when a corner from Frecklington found the head of Beevers. The midfielder beat Barnes only for Gary Croft to clear off the line.