Needing to win to stay in finals contention, the Warriors led 6-0 early on Sunday afternoon but otherwise failed to land a punch as they conceded eight unanswered tries.
They also lost Gerard Beale to a serious knee injury early, while Jazz Tevaga might be suspended for a late shoulder charge on Cronk.
Tevaga was sin-binned for the hit and, while Cronk initially remained grounded, he played on without any real concerns.
For the Roosters, Mitchell finished with a tally of 18 points, including a double to take him to the top of the NRL's try-scoring list with 17 for the season.
Already well clear on the points-scoring list, Mitchell is on track to become the first player since Mal Meninga in 1990 to top both charts at season's end.
The 22-year-old combined perfectly with Luke Keary on the Roosters' left edge as the defending premiers moved two points clear into second spot.
Mitchell scored the tricolours' first try in the 18th minute when Jared Waerea-Hargreaves threw a long offload to strip the Warriors for numbers on the left.
Waerea-Hargreaves was immense in both attack and defence for the Roosters with 144 metres, but might find himself in strife for a crusher tackle.
After Joseph Manu put the Roosters ahead 12-6 at halftime, Mitchell and Keary made an immediate impact at the start of the second half.
Keary was the beneficiary, showing and going before finding Mitchell free on the left, before the five-eighth trailed through on the inside to score.
They were at it again later, when Keary took the ball to the line and found a sprinting Mitchell to score.
The Roosters regularly caught the Warriors out for numbers on both sides of the field, with Brett Morris also wreaking havoc on the right wing.
The veteran also scored once in the second half, albeit after the ball bounced off Cooper Cronk's head as the halfback chased through a Keary bomb.
James Tedesco also scored untouched from a tap to go with his 198 metres and eight tackle busts, while Daniel Tupou and Mitch Aubusson also crossed in the second half.