Wests added another try before half-time from Chris Lawrence but the Roosters regained control with a score from Kiwi winger Sean Kenny-Dowall.
Braith Anasta raced over for the Roosters but the Tigers killed the game off in a dominant second half with additional scores for Tuiaki and Lawrence.
Tries: Dean Collis, Chris Lawrence 2, Robbie Farah, Beau Ryan, Taniela
Tuiaki, Tim Moltzen
Goals: Benji Marshall 6
Tries: Mitchell Aubusson 2, Shaun Kenny-Dowall, Braith Anasta
Goals: Craig Fitzgibbon 4