Rimington beat East Lancashire League leaders Mill Hill for the second time in a fortnight to move to within seven points with four games in hand.
Mill Hill opened the scoring after 15 minutes when the Tangerines failed to deal with a free kick into the area.
This seemed to bring Rimington to life, pressuring the Mill Hill defence into hasty clearances and not allowing them to settle on the ball.
Within five minutes they were level from a corner, as the ball ricocheted around the six-yard box until a Mill Hill defender poked the ball into his own net.
In the second half, a Mill Hill free kick clipped the bar, Graeme Kershaw tipped another free kick onto the post, and Kershaw conceded a penalty before then saving it.
With 20 minutes remaining, substitute Glen Dinsdale picked up the ball in the centre circle and set off on a driving run, before letting fly from 20 yards out, finding the top corner for the winner.