Rimington scored a late, late goal to secure all three points to maintain their bid to retain the East Lancashire League title.
The visitors began well, Benfield finding Dinsdale whose header was blocked, and his follow-up shot deflected past a post.
Dinsdale then saw his header cleared off the line.
Next to try his luck was fullback Rawcliffe, combining with Fagan before firing a left foot shot over, and the latter almost broke the deadlock just before half-time as he curled one just over.
In the second half, Benfield cut in before setting up Fagan, but he saw his effort sail over, and then Dinsdale headed into the path of Bagot, but he too failed to hit the target.
Just after the hour, Hickling headed just wide of the post, before the home side created their only real chance, as Kershaw had to dive to his left to tip the effort around a post.
The champions sealed the win in the dying minutes, as Kershaw pumped the ball downfield and the centre half totally mis-judged the kick and Hickling nipped in to loop a clever header over the keeper.