The decisive boot was set up after the Ravens took over at their own 40-yard line and Joe Flacco connected with Torrey Smith on a key, 14-yard gain.
Baltimore (3-2) had trailed 13-6 halftime, then scored 17 straight points before the Dolphins pulled even in the fourth quarter when Reshad Jones picked off a Flacco pass and returned it 25 yards for a touchdown.
Miami rookie Caleb Sturgis missed a potential score-tying 57-yard attempt in the final minute, sealing the Ravens' victory.
Flacco completed 19-of-32 for 269 yards while Ray Rice netted a pair of rushing touchdowns, picking up 74 yards on 27 carries.
Ryan Tannehill racked up 307 aerial yards with a TD pass on 21-of-40 efficiency for the Dolphins (3-2).
Mike Wallace ran for 105 yards on seven tries for Miami.
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'
Couple mistakenly served bag of cash at McDonald's drive-thru