Man of the match Cordner bent back the Broncos defensive line all night and scored a deserved try in the 62nd minute.
Copley's second four-pointer five minutes later all but sealed the win for the Roosters.
Darius Boyd scored eight minutes from time before Herman Ese'ese was controversially disallowed a try of his own by the bunker two minutes, as they ruled it a double movement, a decision that ended any chance of a late Brisbane comeback.
But it was a deserved victory for the Roosters who enjoyed their best win of a disappointing year.
The Roosters held a lion's share of possession early and led 6-0 after five minutes courtesy of a Copley try set up by a Blake Ferguson pass.
Jarrod Wallace hit back for the Broncos via a kick deflection for a score of 6-all after 19 minutes.
A Latrell Mitchell try from a Connor Watson offload put the home side ahead again in the 27th minute.
Ferguson then scored himself in the 32nd minute when Copley broke the Roosters line and the home side enjoyed an 18-6 lead at the break.
After halftime Shaun Kenny-Dowall and Tom Opacic traded tries before the Roosters won the crucial moments when the game was in the balance to break a six-game losing streak.
Coach Wayne Bennett said the Broncos struggled without representative stars Josh McGuire, Sam Thaiday and Matt Gillett and the loss of Lachlan Maranta due to concussion early hit them hard.
"We missed three Australian players, they are a bit better than a few good ones," he said.
"To be short an outside back, it impacts across the whole situation.Bennett declined to expand on what he thought the Broncos' ongoing problems were.
"It is what it is," was all he offered.
However he said they still had a chance to make an impact this season.
"We are not thinking about the premiership and the top four. We need to get some momentum over the last five games leading into the finals."
Bennett wasn't impressed with the no try ruling against Ese'ese.
"That's why the punters get so upset," he said.
Roosters coach Trent Robinson said the win was a result of weeks of hard work after they had pressed top two sides Cronulla and Melbourne in recent weeks but lost.
"We probably played better in the last couple of games," Robinson said.
"I thought we worked hard for it in the first half and relied on some individual stuff in the second half.
"The footy is there but there is still some stuff as to why we are not in the eight and why we are not contenders this year. If we could make the eight I don't think we would contend."
"I have come to terms why we are in the place we are in. We have paid for our sins. We have been playing some really good footy without winning, but we won tonight.
Copley was dropped for last week's loss to Melbourne but Robinson said he was always going to play him against his old club.
"I thought he was great tonight," Robinson said.
- AAP
