The result left the Browns, who closed the season with a four-game win streak, with a 5-11 record and Jacksonville at 7-9. The loss ended the Jaguars' slim hopes of reaching the playoffs.
Cribbs ran 14 yards for a score in second quarter and Harrison turned in a 6-yard TD run in the third. Dawson's kicks were from 27, 21 and 33 yards.
Harrison totaled 127 yards rushing.
David Garrard completed 22-of-39 passes for for 202 yards and two touchdowns for the Jaguars. Garrard was intercepted twice, once on the final play of the game.