Grimmer, on loan from Fulham, headed home early in the second half to extend Vale's unbeaten home run to six matches.
Defences were on top in the early stages before Gary Harkins squandered a great chance for the visitors when he screwed his shot wide.
Vale responded with a Tom Pope shot, which was deflected off target before the home side suffered a blow with a serious injury to debutant Florent Cuvelier.
The Belgian midfielder, on loan from Sheffield United, collapsed in agony after turning his knee and was stretchered off and replaced by Chris Shuker.
Vale were fortunate to escape a mighty scramble in their penalty area in the last minute of the first half when Harkins squandered the best of three chances.
But the home side made a positive start to the second half and took a 52nd-minute lead.
The unmarked Grimmer headed Shuker's right-wing corner inside Mark Oxley's right-hand post from eight yards.
Jennison Myrie-Williamson should have put Vale in the comfort zone when his 65th minute penalty was brilliantly saved by Oxley following James Dayton's trip on Pope.