The Tigers trailed 8-0 early as Roosters halfback Sam Walker caused havoc but coach Michael Maguire would have been pleased by his side's defensive resolve before they piled on two late tries to snatch victory.
Rival props James Tamou and Lindsay Collins were placed on report for dangerous contact and are in doubt for the opening round.
However, there were no major injury concerns in an entertaining yet low scoring match, in which Walker, Joey Manu and Victor Radley impressed for the Roosters, while Jackson Hastings made a strong debut for the Tigers.