"Nobody has such a high opinion of me as a quarterback," said Harbaugh, who closed a 21-point gap for the second time this season. "I'll never be a Dan Marino or a Joe Montana. I just do it in my own ugly style."
Ugly or not, it worked.
Harbaugh finished 25 for 33 for 319 yards and three touchdowns and seized the spotlight on the day Marino eclipsed Fran Tarkenton's record for pass completions.
With Cary Blanchard's 27-yard field goal on the first drive of overtime, Indianapolis completed a comeback that began with a 24-3 halftime disadvantage.
In the third quarter, Indianapolis converted two fourth downs and drove 85 yards to set up Harbaugh's three-yard pass to Floyd Turner. Turner later caught a 45-yard pass to make it 24-17.
Harbaugh then threw to Aaron Bailey for 21 yards to send the game into overtime.
"It's a tough loss for us, to see our unbeaten streak go down the drain in a game like this that we completely dominated in the first half, and then to come apart the way we did in the second half is just an embarrassment to us," Dolphins Coach Don Shula said.
Marino's six-yard pass to Keith Byars in the second quarter was the 3,687th completion of his career--one more than achieved by Tarkenton during his 18 seasons with the Minnesota Vikings and New York Giants.
Tarkenton threw 342 touchdown passes, passed for 47,003 yards and had 6,467 attempts.
Through Sunday's game, Marino, in his 13th season, has 336 touchdown passes, 46,443 yards, 6,200 attempts and 3,702 completions. In 1993, he played only five games and underwent surgery to repair a torn right Achilles' tendon.
The game was delayed two minutes for a standing ovation and a videotaped congratulatory message from Tarkenton.
"It's nice, but it kind of takes it away when you lose like this," said Marino, who was 19 for 30 for 194 yards. "It's something I'll think about and cherish, but later. It's a good thing it came early in the game."
Said the Colts' Turner: "He's one of the greatest to ever play the game, but we can't give him the game just because he got the record."
The Colts' comeback was not unfamiliar. In the second game this season, Harbaugh replaced Craig Erickson with the Colts down, 24-3, to lead them to victory over the Jets.
Indianapolis also spoiled an undefeated record for the second time this year. The Colts handed St. Louis its first loss last week, 21-18.
The Dolphins, who scored on each of their first four possessions, appeared to have the game in hand at halftime behind Terry Kirby's scoring runs of two and three yards and a five-yard touchdown reception by Irving Spikes.
In the week before the game, Miami's attention was focused on stopping the Colts' Marshall Faulk, who was never a threat. A swarming Miami defense held last year's offensive rookie of the year to only 42 yards rushing and 17 yards receiving.
Faulk, who had 177 yards last week against the Rams, fumbled the ball on the Colts' 34-yard line, setting up Kirby's first score.
"Marshall is not going to win every game for us at the end," Colt Coach Ted Marchibroda said.
Though much of the game's attention was focused on the quarterbacks, the kicking game also was crucial.
On the first drive of the overtime, Harbaugh marched the Colts downfield to set up Blanchard's 27-yard field goal. It was Blanchard's first game as a Colt.
Pete Stoyanovich missed a 49-yard field-goal attempt with 12 seconds remaining that would have won the game for the Dolphins. Earlier he hit from 51 yards and missed from 27.
"Everything was pretty good, the snap, the hold, the placement," Stoyanovich said of the final attempt. "That's the kind of kick I'm supposed to make. I'm just embarrassed."