Down 16-0 with half an hour to go in the NRL clash at Eden Park on Saturday night, the Warriors scored through Shaun Johnson, Pita Godinet and Bill Tupou.
But Johnson mishit his sideline conversion of Tupou's 75th-minute try to leave the Warriors short and keep them winless after two rounds.
Much of the pre-match attention had been on Sonny Bill Williams and his second match back in the NRL.
Williams was again solid and did produce one magic late offload that led to centre Michael Jennings almost scoring what would have been the victory-sealing try.
Williams was also involved in a couple of skirmishes with young centre Konrad Hurrell that brought the crowd alive.
Early in the first half, he took exception to being pushed as he was running back into position for a restart.
The part-time boxer turned and shaped up to Hurrell, only to be held back by Warriors prop Sam Rapira.
Minutes later, when Hurrell ran at him, Williams pulled off what seemed like a fair strip of the ball, only for the Roosters to be penalised for a two-man tackle.
But two Hurrell errors early in the second half were to prove decisive.
A play-the-ball penalty gave the Roosters the field position to send substitute Mitchell Aubusson over with some nice footwork.
Hurrell then lost possession in a tackle deep in his own territory and the visitors again capitalised with centre Shaun Kenny-Dowall touching down for a 16-0 lead.
That was the signal for a Warriors fightback.
They received a break deep in defence when Roosters fullback Anthony Minichiello couldn't hold a pass and Johnson scored from an 80-metre run.
Godinet then produced a piece of individual magic to force his way over from dummy-half, with Johnson's conversion making it a six-point game.
Johnson was the architect when the home side scored again, his kick-ahead chased down by winger Bill Tupou.
Earlier, the Roosters split the game open in the fifth minute thanks to a superb sideline break by Jennings.
The ball was worked to Minichiello, who finished in fine style despite some frantic cover defence from Warriors skipper Simon Mannering.
James Maloney's conversion made it 6-0 and heralded a period of Roosters dominance.
The Warriors held out and then began to get into the contest, but they struggled to make their attack click.
Three times, they were in strong field position and three times, they were stopped by errors.
While the match attracted 32,740, the figure was lower than the attendances for the two previous Warriors fixtures at Eden Park, with the record being 38,412 two years ago.