Coles began the revival skimming in a second-half header from a corner.
It was a goal he owed Rovers for early in the half he had helped a 35-yard speculative cross from Jason Demetriou past his own keeper.
His goal brought Rovers to life, but it was Coles' last touch for minutes later he was hobbling off with a knee injury.
But Rovers were now in full flight and on 70 minutes took the lead as Hinton hustled in a Stuart Campbell free-kick.
They just about held on surviving a barrage of corners, seven minutes added on time and the loss of coach Paul Trollope, who was sent to the stands for the second time this season.
Rovers went into the game with the safety first set-up with Campbell sitting just in front of the back four.
Without wingers they had a very narrow look, while by contrast Leyton were sharper on the break and saw JJ Melligan almost giving them an early lead.
Goalkeeper Steve Phillips just managed to fish the ball out from under the angle of the bar, but was not troubled again in the half. His left-back Aaron Lescott, doubling up as a winger, had a much busier time.
One long crossfield run brought Rovers a corner which saw Darryl Duffy send a header just wide of the far post.
Lescott then initiated his side's best move which brought both Duffy and his partner Rickie Lambert into an inventive raid, which ended with Craig Disley missing his kick.
His misery was shared later by Melligan, who found it difficult to believe he so badly mistimed the volley after Ryan Jarvis and Adam Boyd had cut open the home defence.