Three first-half goals, including two inside a minute, set up the victory for an impressive Chester who moved to fourth in the table.
The home side should have taken the lead as early as the fourth minute, when Scott McNiven's cross found Stewart Drummond in front of goal, but the midfielder's free header just cleared the bar.
The game swung decisively Chester's way with two quick goals. First, on 34 minutes, the Rovers defence only half-cleared a corner and Ryan Lowe struck the ball home, with his shot taking a deflection on its way past Scott Shearer.
And before the visitors had recovered, a free-kick swung in by Ben Davies was deftly nodded in by David Artell.
The game was made safe in first-half added time when Marcus Richardson met Scott McNiven's right-wing cross with a superb diving header into the bottom corner.
The second half inevitably petered out, with Chester content to hold on to their advantage and Rovers unable to break through, leading the away fans to start calling for the head of manager Atkins.
Gregg Blundell's strike three minutes from time, after Artell's efforts had come back off the bar, only added insult to injury for the traveling faithful.