After an eighth minute James Maloney penalty goal, Peter Mata'utia crossed for the first try of the match. Blake Ferguson was crunched in a tackle from Jason Nightingale for Mata'utia to scoop up the loose Steeden and crash over.
But that went against the run of play for the first half, with the Roosters responding through Kenny-Dowall in the 15th minute after he latched onto a James Maloney kick.
The Roosters dominated up front through much of the first half and interchange prop Kane Evans continued that trend when he scored from close range next to the posts in the 28th minute for the Roosters to lead 14-6 with the Maloney conversion.
A late Gareth Widdop penalty goal brought the scores closer just before halftime.
Kenny-Dowall crossed for his second in the 58th minute from a Roger Tuivasa-Sheck pass, his 105th four-pointer for the Roosters.
The try put Kenny-Dowall past Bill Mullins as the tricolours' second all-time try scorer behind Anthony Minichiello (139 tries).
The Roosters looked to be cruising to a comfortable win before Widdop crossed on the end of a scintillating 80m effort to drag his side to within four points.
An 80th minute field goal from Jake Friend pushed that gap out to five as the Roosters held firm and recorded their eighth win of the season.
Roosters coach Trent Robinson said the win was all the more impressive from a side without starting props Jared Waerea-Hargreaves (calf), Sam Moa (suspension) and star centre Michael Jennings (stood down).
"We had to tough it all the way," he said.
"I thought the boys did a real good job, there were some good touches in the last five minutes. We could have gone into our shell but we didn't."
Robinson said however his side did lack "rhythm" in attack and praised the effort of Kenny-Dowall.
"He was huge, the kind of game he had was great," Robinson said.
Dragons coach Paul McGregor said his side's first half defensive effort told in the end.
"We were right in it to the death, but that first half took a lot of gas out of us," he said.
"We just couldn't get any field position and that was on the back of our kicking game."
Mata'utia (knee) captain Ben Creagh (sternum) and Jason Nightingale (knee/ankle) are all injury worries for the Dragons.
- AAP