A goal from Brazilian Santos Gaia was enough to send Exeter through to the second round of the FA Cup.
Exeter created a string of chances and fully deserved the win.
Grimsby created little and can have few complaints about crashing out of the cup at the first hurdle.
Exeter forced four corners in a row and took the lead in the sixth minute.
Andy Taylor's corner was flicked on by Steve Flack and Santos Gaia stabbed home his seventh goal of the season from five yards.
It was the perfect start for the Grecians. Grimsby were poor for most of the first half and barely seemed interested in progressing in the FA Cup.
It took 24 minutes before Grimsby had their first attempt on goal. Andy Parkinson ran on to a long ball and saw his shot from 12 yards tipped wide by Martin Rice.
Danny Clay could have stretched the lead for Exeter two minutes later. He was found inside the box by Sean Devine but miscued his shot.
Exeter looked a threat going forward and grew in confidence as the half wore on.
Les Afful twice struck the ball over the bar as Exeter continued to look the more likely to score.
After the break Afful ran on to a long ball and sprinted into the box but was denied by a lunging tackle as he prepared to strike.
The game finally began to resemble an FA Cup tie as the challenges began to fly in and there were four players booked in the first 15 minutes of the second half.
Grimsby did their prospects no good at all when Michael Reddy was shown red after picking up his second booking for kicking the ball away.
Dean Gordon came close to equalising when his long range shot hit the bar but Exeter held on for a deserved win.