Rovers grabbed the early goal and were then able to hold on to frustrate an out of sorts home side.
Chester had a few early half chances notably when marksman Daryl Clare guided a header into the hands of Steve Perrin and was then only inches away from getting a touch on Wayne Hatswell's cross, but aside from that there was little for the Blues fans to shout about.
On 18 minutes the visitors scored the all-important goal when Ben Cleverley played a superb ball over the top as the Chester defence went absent, and Alex Meechan made no mistake with a delightful lob over Wayne Brown.
Chester looked to respond and on 25 minutes Ryan Sugden found the sidenetting after latching on to a cross from the right.
The home side should have put themselves on level terms in the 33rd minute when Ben Davies completely missed a free header as Kevin McIntyre's cross flew across the face of goal.
Keeper Perrin produced one blinding save before the interval, blocking Clare's shot when the striker was clean through on goal.
The restart saw Chester on the offensive and they felt aggrieved when Steve Jenkins, who was clearly the last line of defence, pulled back Sugden but only received a yellow card for his indiscretion.
Carl Ruffer saw a goalbound header cleared off the line by Martin Foster just before Mark Wright shuffled his pack, with Mark Beesley and Michael Twiss replacing Jimmy Kelly and Sugden.
Fighting almost exclusively a rearguard action, Rovers produced one bright moment in the second period when Gary Owers hit a powerful shot that stung the hands of Brown.
Ten minutes from time Beesley wasted the best chance to level, shooting straight at the keeper when only eight yards out.