The 86-yard drive that ended in the winning score was set up by Brock Marion's interception of an ill-advised third-down pass by Manning with just under three minutes to go.
And the Miami defense, with Zach Thomas back at middle linebacker after missing five of the last six games, held the Colts to their lowest point total of the season and Manning to his second-lowest yardage total, 209.
"We have a lot of pride in our defense," Thomas said. "If Brock Marion does not intercept that ball, we probably don't win."
"The Colts have a lot of firepower. To just give up 14 points to a team with the firepower they have, we're extremely excited," Miami linebacker Robert Jones said.
For the Colts, it was the third loss in their last four games, two of them cold-weather road games in Chicago and Green Bay. They have to go back outside against the Jets in the Meadowlands next week, a game that is now vital to their playoff hopes.
The Dolphins entered the game without quarterback Jay Fiedler and running back Lamar Smith, two of their most important offensive playes. That left it to Huard, who won five of six games last year in place of the now-retired Dan Marino. But he threw for just 128 yards and threw three interceptions after Fiedler was injured in a loss to the Jets.
The Colts took the lead on two TD passes from Manning to Marvin Harrison, one from 28 yards in the first quarter and another from 8 yards. The first came on their first possession of the game, the second on the second play of the final period to take a 14-10 lead.
Indianapolis seemed to be on the way to the win when it got the ball with 8:24 left. It nibbled 4 1/2 minutes off the clock, led by Edgerrin James, who carried 26 times for 118 yards.
But on third-and-7, instead of running to eat up time and set up a field goal, Manning threw deep over the middle, Marion got in front of Jerome Pathon and grabbed the ball.
"I threw it behind Jerome and the safety was right there," said Manning, who was 16-of-34 for 209 yards.
The Dolphins started from their own 14, and Huard was at his best 6-of-7 for 77 yards on the drive.
"Deep down, you want to feel like a contributor. That's what it's all about," said Huard, who finished 22-of-33 for 184 yards. "I've had success throughout my career with the 2-minute drill. We really get into a rhythm. You stop thinking and start throwing."
Indianapolis had one last chance. When Manning hit Harrison for 25 yards on the first play of their final possession, it looked like the Colts would at least tie the game.
But they couldn't get beyond the Miami 42. And Mike Vanderjagt finally had to try a 59-yard field goal that was deflected at the line of scrimmage.
"It was all we could do," Colts coach Jim Mora said. "I told him, 'Just go out and kick the sucker.' He didn't feel real confident about it."
The Colts led 7-3 at the half, taking the lead on their first possession on Manning's 27-yard pass to Harrison on a deep slant.
The Dolphins scored on their last possession of the half, getting a 28-yard field goal by Olindo Mare after some curious play-calling runs on second-and-2 from the Indianapolis 11 and third-and-1 from the 10, the latter with 29 seconds and no timeouts left.
But the Dolphins came right back on the first drive of the second half, eating up half the third quarter to go 74 yards in 13 plays, with Johnson going in from 3 yards out to give th Dolphins their first lead of the game.
Thanks to the defense, they got their second and final lead.
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