Jones struck on 22 minutes after good work from Andy Parkinson and former Sheffield United midfielder Curtis Woodhouse set him up eight yards from goal.
The Town striker kept his cool to side foot the ball past Lincoln keeper Alan Marriott.
Lincoln came close to grabbing an injury-time equaliser when a last-ditch effort from former Huddersfield defender Nat Brown was cleared off the line by Woodhouse.
The rebound fell to central defender Gareth McAuley, whose shot came back off the bar.
The first chance of the game fell to Lincoln striker Jamie Forrester whose 25-yard free-kick was firmly struck into the Grimsby wall on six minutes.
Referee Lee Mason disallowed two Lincoln goals in four minutes, the first for pushing by Lincoln captain Jamie McCombe after his header beat keeper Steve Mildenhall.
Former Derby striker Marvin Robinson saw a close-range effort ruled out for offside just a minute before Jones grabbed the vital strike for Grimsby.
As desperate Lincoln went searching for the equaliser, Brown headed wide from a Jeff Hughes corner.
Milldenhall then had to be at his best to save a 31st minute free-kick from Hughes, diving well to his left-hand post.
Grimsby nearly grabbed a second four minutes into the second half when a 30-yard chip from Paul Bolland struck the crossbar.
Only a desperate challenge from Red Imps defender Lee Beevers stopped Gary Cohen slotting home the rebound.
Lincoln again went close when Francis Green shot wide after a good move down the left.
But Grimsby missed another great chance to score a vital second goal when Parkinson went close with a curling right-footed shot on 89 minutes.