And there was a 14th of the campaign for striker Rickie Lambert who made sure of the points ten minutes from time.
Cheltenham were handed a lifeline on 87 minutes when Danny Coles was penalised for shirt-tugging. But Steven Gillespie fired his penalty against a post.
Hinton's 40th minute goal followed a free-kick from just inside the Rovers half. Lambert got his head to the ball to knock it down into the path of his team-mate who volleyed home from eight yards.
Rovers deserved their half-time lead having created all the clear chances. Cheltenham keeper Shane Higgs did well to parry a fierce shot from Andy Williams in the 20th minute.
Williams also shot wide from a good position and Lambert volleyed over from another clear opportunity.
The game became more spicy in the second half and there were bookings in the space of 15 minutes for Cheltenham's Alex Russell and Damian Spencer, along with Craig Disley of Rovers.
It was a disappointing night for the visiting strike force of Spencer and Gillespie, both ex-Bristol City players who were jeered by the Rovers fans for much of the game.
But Cheltenham were enjoying their best spell when the game was effectively decided by a free-kick decision on 81 minutes.
Gavin Caines toe-poked the ball in the direction of goalkeeper Higgs, who elected to grab it rather then boot it clear. Referee Mason saw it as a back-pass and Rovers were given the opportunity of an indirect free-kick virtually on the penalty spot.
The ball was tapped into the path of Lambert who unleashed a low shot through the wall and into the net.