The visitors, yet to win away from home this season, went down to first-half goals from Kevin Sandwith and the impressive Roberto Martinez.
Chester were forced into an early change as Ashley Westwood limped out of the action after only ten minutes, being replaced by Graham Allen, who made his debut for the Blues.
The home side made most of the early running and penned the visitors in their own half for the majority of the first 15 minutes.
And it was well deserved when Chester took the lead on 18 minutes as a beautifully taken free-kick from around 25 yards by Sandwith was touched by the keeper onto the post and crept over the line for the opener.
Before the home fans had even finished celebrating the goal, Rovers almost pulled level when a shot from inside the box from Rickie Lambert was deflected by Chester keeper John Danby onto the post and then away to safety.
The advantage was doubled eight minutes before the interval with a delightful goal from Martinez.
The Spanish midfielder, who was superb throughout, received the ball from Jon Walters just inside the box and executed a brilliant chip over Rovers keeper Steve Phillips which clipped the post on its way into the net.
Rovers were short of attacking ideas and showed little sign of ending their poor record away from home as Chester bossed the game from start to finish.
Gregg Blundell shot wide from a difficult angle, and both Sandwith and Walters fired efforts just past the post as the home side maintained the upper hand in the second period.
Just after the hour mark, Walters nodded the ball in to the path of Blundell but his header was weak and straight at the keeper.
The visitors briefly threatened the Chester goal when substitute Craig Disley headed an effort goalwards, but the ball was clutched under his crossbar by Danby.
And their miserable day was complete when Disley blazed over the bar from ten yards out when the goal was at his mercy.