Lee Blackett’s side won six tries to three thanks to braces from Jack Preece and Sean Scanlon and further scores by Michael Keating and Curtis Wilson.
Titans’ game-management was excellent, particularly the kicking of fly-half James McKinney.
Contrastingly, error-strewn and indisiplined Carnegie lost for the fourth Yorkshire derby in a row in the league this season.
Captain Ryan Burrows scored a hat-trick of tries but the penalty count killed any chance they had of making a game of it.
It left head coach Tommy McGee searching for answers in the aftermath.
Watch his reaction here, and for the report read Sports Monday, free inside The Yorkshire Post.