Despite the Patriots' having already clinched the AFC East title for the fifth time in the past six seasons, Brady played into the early portion of the fourth quarter and completed 15-of-24 pass attempts.
Vinny Testaverde capped the game's scoring with a six-yard touchdown pass to Troy Brown in the final minutes. That gave Testaverde a TD pass in 20 straight seasons, an NFL record.
Dillon had 67 yards rushing and Laurence Maroney had 73. Reche Caldwell caught four passes for 134 yards.
The win gave New England (12-4) -- winner in six of its last seven games -- a chance at the third seed in the AFC playoffs.
Vince Young passed for 227 yards for the Titans (8-8).