Hooker Beau Falloon extended the lead with a try under the posts five minutes later with Aidan Sezer adding the extras to put his side 12-0 in front.
The Roosters hit back through Mitch Aubusson and on the stroke of halftime Mitchell Pearce's effort was given the green light by the video referee after his initial effort had been ruled out by the on-field officials.
But the expected second half onslaught never materialised after the break when young winger Anthony Don raced 60 metres following a Takairangi offload and increased the Titans' advantage.
That setback did kick the Roosters into life and Jennings had an effort ruled out by the video referee before Daniel Tupou demonstrated some great athleticism to haul in a James Maloney kick and jink his way to the line.
Prop Sam Moa then put the hosts in front for the first time in the game when he rumbled over from close range after being teed up by Williams.
However, Takairangi and Taylor had the last laugh to keep Cartwright's's side in the hunt for a top-eight spot going into the final round of the season.
-AAP