Cheltenham were completely outclassed but they stuck to their task throughout and missed chances to make the scoreline more respectable.
Rovers were slack at times in defence but enjoyed so much possession they looked as if they could have moved up several gears if necessary.
Town keeper Scott Brown made a brave save at the feet of James Coppinger as Rovers set the pattern for the game as early as the third minute.
Brown did well to tip a powerful 20 yarder from James O'Connor over the bar four minutes later before John Spicer cut inside to have a low shot saved in the 7th minute.
It was virtually one-way traffic and Rovers made the breakthrough they deserved following a free-kick in the 26th minute.
Martin Woods' cracking effort from 20 yards was pushed onto the crossbar by Brown, but the ball bounced out to Brian Stock who tapped home from close range.
Brown was at full stretch to save from Lewis Guy in the 31st minute before Rovers increased their lead five minutes later.
Spicer hit a fierce shot which was blocked on the line following a corner from Woods and defender Sam Hird followed up to fire home his first goal for the club.
The pattern continued after the interval, although Ashley Vincent twice missed golden opportunities to put Cheltenham back in the match.
Stock notched his second and Rovers' third when he hammered home from 25 yards in the 58th minute after Coppinger had seen a fierce effort blocked.
Substitute Jonny Hayes missed another good chance for Cheltenham when he headed wide in the 64th minute, but Rovers were dominant and Stock was unlucky not to complete his hat-trick when he rocketed a shot against the crossbar from 25 yards two minutes from time.