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.