A free-kick from captain Lee Peacock after 38 minutes sealed the win against a side who were reduced to 10 men for the incident that led to the set-piece.
Michel Kuipers was sent off after handling the ball outside the area, and the wall from the ensuing set-piece left a huge gap for Peacock to slot the ball home.
That was the only clear chance created in the match by a Mariners side who were far from their best, but inspired by a dogged defence.