Title hopefuls Rimington slipped to their first East Lancashire League defeat of the season against Read.
Read went ahead after 15 minutes when a corner was only half cleared, and a cross was rammed home.
Worse was to come for the home side when another defensive lapse gave Read time and space to make it 2-0 from the edge of the area.
Rimington responded, and on 35 minutes Dinsdale poked home from a corner.
But before half-time, Benfield lobbed the ball back to Kershaw, but it squirmed off his thigh and trickled into the corner of his net.
McLean pulled one back with 15 minutes remaining as his free-kick floated over everyone to find the top corner.
However, Read made sure of the points in the last minute, as a cross was slammed in at the second attempt.
Rimington boss Terry Baithwaite said: “Our first defeat could be crucial as it gives Burnley the chance to win the league.”