Chances were few and far between in a tight local derby, although Anthony Pulis went close for Lincoln with a long-range shot in the 27th minute.
Grimsby's Peter Sweeney had a penalty shout turned down, but neither goalkeeper had a serious save to make in the first half.
Grimsby centre-back Paul Linwood had a great chance to break the deadlock in the 59th minute, but he put his header wide from close range. Lincoln produced a rare attack in the 63rd minute and Jamie Clarke blasted in a shot that was beaten away by Nick Colgan.
Adam Watts had an effort cleared off the line as Lincoln pressed for an undeserved winner and he was later stretchered off after a collision with Joe Widdowson, who was also forced off the field.