Late in regulation, Mare had missed a 48-yard field goal, not only preventing the Dolphins from taking the lead but also giving Baltimore an opportunity for a short drive to break a 6-6 tie.
But the defense rose that time, as it did throughout the afternoon.
After Baltimore marched into Miami territory, the Dolphins forced the Ravens to punt.
The Dolphins took over at their own 20-yard line with 51 seconds and three timeouts remaining, but Coach Dave Wannstedt elected to run Ricky Williams twice as the crowd at Pro Player Stadium loudly booed the conservative approach.
Wannstedt's decision paid off in the end because Zach Thomas was able to recover a Jamal Lewis fumble at the Baltimore 33-yard line to set up Mare's game-winner.
It was the third takeaway for the Dolphins defense, which also got a Sam Madison interception in the second quarter and a Sammy Knight pick in the fourth.
The Madison interception set up Mare's first field goal, from 23 yards out.
But Lamont Brightful's 73-yard return on the ensuing kickoff helped the Ravens quickly tie the score at 3-3.
The Dolphins regained the lead 6-3 on Mare's 52-yard field goal in the third quarter to cap a drive that was aided by two questionable penalties that gave them 28 yards.
Baltimore tied it 6-6 early in the fourth quarter on Matt Stover's 45-yard field goal.
The Ravens got their biggest chance when safety Ed Reed picked off Brian Griese and returned the ball to the Miami 36-yard line.
But two plays later Knight picked off quarterback Anthony Wright to end the threat.