Johnson rushed for 136 yards on 19 carries and White gained 99 yards on 24 carries as the Titans secured the AFC South Division title for the first time since 2002.
Phil Dawson scored Cleveland's points with three field goals.
Ken Dorsey went 22-of-43 for 150 yards and one interception, but Jamal Lewis was limited to just 7 yards on seven carries in the Browns' third loss in a row.
Dorsey was marking his first start since November 2005, when he played for San Francisco, and only the 11th start in his six-year NFL career.
Celebrity Families of 2014 [PHOTOS]