The improbable win came after the Titans had blown a 24-9 third-quarter advantage.
Vince Young threw 3 touchdown passes and ended with 236 passing yards with 1 interception.
Chris Johnson gained 159 all-purpose yards -- 104 rushing and 55 receiving.
Bironas kicked 2 field goals, while Justin Gage caught 2 scoring passes for the Titans (7-7), who have won seven of eight.
Miami's Chad Henne threw for 349 yards, 1 touchdown and 3 interceptions.
Ricky Williams rushed for 80 yards on 19 carries with 1 touchdown.
He eclipsed the 1,000-yard rushing mark for the fifth time in his career.
Williams also had a 2-point conversion run and lost a fumble, while Dan Carpenter kicked 3 field goals for the Dolphins (7-7), who barely maintain AFC playoff hopes.