The Titans appeared to be heading for defeat after a fourth-quarter meltdown gifted two touchdowns to Miami who surged into a 27-13 lead with four minutes and 34 seconds remaining.
But Titans rookie quarterback Will Levis responded superbly to orchestrate two late touchdown drives that saw the visitors sneak to victory.
Levis found DeAndre Hopkins with a three-yard pass to cap a 75-yard drive to cut the gap to 27-19, and then made a successful two-point conversion to make it a one-score game.
Tennessee then forced Miami to punt, allowing Levis to launch another long drive that culminated with running back Derrick Henry charging over from three yards to make it 28-27 after the extra point.
There was still time for Miami to attempt to get into field-goal range, but the Titans defence bottled up Tua Tagovailoa as the Dolphins turned over to effectively end the game.
"I think we showed the type of team we always thought we could be this season," Levis told ESPN.
"Obviously we've had some lows but we've got a special locker room and special guys across the board. So glad that we were able to grind it out at the end there."
The Titans remain bottom of the AFC South with a 5-8 record and have little realistic prospect of forcing their way into the postseason.
But the defeat could prove costly for Miami, who would have drawn level with the Baltimore Ravens at 10-3 with the best record in the AFC with a victory.
Instead, the Dolphins fell to 9-4 to leave the Ravens on pole position for top seeding and home-field advantage in the play-offs.
A Miami defeat had seemed unthinkable after Tennessee seemingly hit the self-destruct button in the fourth quarter.
A muffed punt reception handed the Dolphins possession in the red zone to allow Raheem Mostert to score the go-ahead touchdown at 20-13.
Levis then botched a pitch on the next Titans possession to hand back the ball to Miami, and Mostert subsequently claimed his second touchdown to leave Miami 27-13 ahead.
But the Titans' unlikely late rally turned the game on its head to leave the Miami home crowd in stunned silence.
Monday's other NFL game also went down to the wire, with the lowly New York Giants upsetting the Green Bay Packers 24-22 at MetLife Stadium in East Rutherford.
Giants kicker Randy Bullock slotted a 37-yard field goal with the final kick of the game to clinch victory for New York, who improved to 5-8.
