With props Jared Waerea-Hargreaves and Matt Lodge leading the way up front and Tedesco typically elusive with nine tackle breaks, the Roosters turned an eight-point half-time lead into their 12th win of the season.
The Roosters needed just four minutes to open the scoring thanks to Joseph Suaalii, who had a saloon passage to the line courtesy of a long cut-out pass from Victor Radley.
Radley was in the thick of the action again in the 17th minute when he put Lodge over next to the posts with a good short ball and the Roosters led 10-0.
The Roosters continued to mount pressure and almost had a third through Joey Manu when he flew high to take a bomb but lost the ball as he tried to get it down.
With seven minutes remaining in the first half the Cowboys hit back when Murray Taulagi showed great strength to crash over in the corner after a brilliant tap-on by Luciano Leilua.
On the back of their second penalty for the day the Roosters worked their way down field where Sam Walker and Paul Momirovski combined to put Daniel Tupou over in the left hand corner.
In the 53rd minute the Roosters went out to a 20-6 lead when Sam Verrills darted over from the back of a scrum close to the line with the Cowboys complaining that Lodge had held Griffin Neame back and prevented him getting a shot at Verrills.
Five minutes later Neame stood tall at the opposite end of the field when he put hooker Reece Robson in for a try with a deft offload.
Waerea-Hargreaves capped an outstanding game when he powered over for the 16th try of his career in the 65th minute and the Roosters led by 14.
When Verrills showed great strength to get over for his second try of the day the Roosters were home and hosed at 32-12.
Hamiso Tabuai-Fidow grabbed a consolation try for the Cowboys with one minute to play but the damage had well and truly been done.
For the time being at least the Roosters have leapfrogged the Broncos into seventh place on the ladder, pending Brisbane's game against the Knights.