Hasselbeck gained 220 yards on 10-of-20 passing efficiency and the Titans logged their first 3-1 start since 2008, when they won 10 straight to begin that season before finishing 13-3.
Chris Johnson picked up 100 rushing yards on 23 carries while Jared Cook chipped in with 93 yards receiving on two catches, including an 80-yard score.
Tennessee's defense also got into the act, with Jonathan Babineaux returning a pick-off 97 yards for a third-quarter touchdown.
Cleveland (2-2) lost despite a fine day from Colt McCoy, who completed 40-of-61 passes for 350 yards and a touchdown.
Peyton Hillis, however, was held to 46 rushing yards on 10 tries.
Texas principal bans speaking Spanish, stirs controversy
Britney Spears on kissing Ryan Gosling, Justin Timberlake in the Mickey Mouse Club