Tim Moltzen then booted the kick-off out on the full and from the resulting penalty, Shaun Kenny-Dowall scored in the right corner to leave the Tigers shellshocked.
Young centre Tautau Moga and Tupou went over before the interval to stretch the advantage further for the hosts, with Anasta, playing his final home game before joining the Tigers next year, kicking three goals.
The second half started in a similar fashion with Mitchell Pearce finishing off a move that had a suspicion of obstruction about it after he ran behind decoy runner Minichiello, to score and end the game as a contest.
Stand-in Tigers skipper Benji Marshall did his best to try and inspire his side, firing a brilliant cut-out pass to Marika Koroibete for the visitors' first try of game and Blake Ayshford scored his fourth of the season shortly after.
But there was to be no second-half capitulation from the Roosters with Tupou grabbing his third after Junior Moors dropped the ball under his own posts from the kick-off.
Minichiello got in on the scoring act 13 minutes from time, much to the delight of the crowd after some unselfish play from Pearce, who crossed the line but flicked a pass so the veteran fullback could touch the ball down.
The Tigers finished with some pride, scoring two late tries as Chris Heighington marked his 200th game with a four-pointer before Ben Murdoch-Masila crossed.
Marshall was put on report for a high shot on Jared Waerea-Hargreaves.
- AAP