Hooker Rowett helped himself to three tries as the in-form Gladiators made history by winning three away games in a row for the first time since the club was formed in 2008.
Prop Chris Young opened Chester's account when he showed good awareness to pick up a loose ball and race over the try line although Rowett's conversion attempt missed the target.
Rowett grabbed his first try of the game on 16 minutes as he scooted over from close range and Luke Edwards successfully landed the goal to put Chester into the lead.
Fitton Hill came back strongly to level the scores before Rowett grabbed his second, again converted by Edwards, to move the Gladiators back in front.
The Bulldogs hit back again but winger Mark Hanson showed good speed on the outside to send Chester into the break on top.
Both sides raised the intensity in the second period with some strong hits and frantic defence.
Steve Sandbach crashed over for the first try of his career to keep Chester's nose in front but Fitton Hill added two penalties to a try of their own to take a four point lead.
With time running out, Rowett again exposed the home side's ruck defence to wrap up his hattrick and Edwards conversion gave the Gladiators the narrowest of leads.
Chester dug deep in the final few minutes to hold for a fine victory that helped them leapfrog the Bulldogs in the table.