Brady completed 24-of-40 passes and fired a touchdown pass to Wes Welker while Ridley picked up 45 of his 71 rushing yards during a fourth-quarter drive that led to a Stephen Gostkowski field goal with 1:10 remaining.
Ridley also scored a touchdown for the Patriots (9-3), who captured the AFC East crown for the 10th time in 12 seasons.
Welker finished with 12 catches for 103 yards.
Rookie Ryan Tannehill completed 13-of-29 passes for 186 yards for the Dolphins (5-7).
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