One of the NFL's most durable quarterbacks, Manning threw three touchdown passes to Marvin Harrison that gave Indianapolis (4-4) a seven-point lead going into the fourth quarter.
But linebacker Zach Thomas returned an interception 17 yards to set up a 31-yard field goal by Olindo Mare, pulling Miami (6-2) within 24-20.
On the next possession, Manning found Harrison for 16 yards just as he was drilled in a helmet-to-helmet hit by defensive end Lorenzo Bromell, who drew a 15-yard penalty and may be looking at a steep fine.
"I didn't think it was a late hit, dude," Bromell said. "I mean, I might get a fine from the league, but to me, that was a great hit."
"I didn't see it. I was looking downfield," said Colts coach Jim Mora, who added that the officials were "below average. I'll probably get fined for that, but I don't give a damn. They're usually below average."
The hit knocked Manning woozy and drew blood from his mouth and lip.
"I don't know what to say. The guy knocked the (bleep) out of me," Manning said. "It's my jaw. It's really sore. They're going to take a look at it right now, get some treatment. I didn't lose any teeth."
On fourth and inches from the Colts 39, Fiedler threw a short pass to Chambers and the rookie raced 10 yards for a first down. On the next play, he found Chambers alone down the left sideline for the go-ahead score.
"We liked the matchup," Chambers said. "I had a lot of room."
Manning returned, but clearly was not the same player. He had two chances to tie or win the game, but the first ended in a punt and the second on a fourth-down incompletion after Taylor sacked him.
Fiedler completed 17 of 29 passes for 269 yards and two scores, both to Chambers, who had three catches for 113 yards. The rookie from Wisconsin is emerging as Fiedler's favorite target.
"It looked like most of the coverages were set up to take away Oronde (fellow receiever Oronde Gadsden)," Chambers said. "He's had some big games against them. That helped open things for me. I got to see some man-to-man (defense)."
In addition to Chambers and Minor, rookie cornerback Jamar Fletcher stepped in after Sam Madison was injured and did well to help contain the lethal passing game of the Colts.
"I thought I played well," Fletcher said. "Obviously, I've got a lot of things to change. I was around the ball, made a few plays. As soon as I come in, I think they are going to throw to me."
"The effort that this team gave today, you couldn't ask for anything more than a coach," Dolphins coach Dave Wannstedt said. "This was a team victory."
Miami has won four straight visits to Indianapolis.
Manning was 20 of 33 for 253 yards and three scores to Harrison, who had nine catches for 174 yards. But Manning also was picked off twice and the Colts were not the same without running back Edgerrin James, who missed his second straight game with a hyperextended left knee.
"It's an extremely disappointing loss," Manning said. "A little bit here and a little bit there and it could have been different."
Rhodes, who ran for 100 yards last week, had 42 on 14 carries.
Minor tiptoed along the right sideline for a 56-yard touchdown run with 2:39 left in the first quarter, erasing a 3-0 deficit.
Early in the second quarter, Harrison caught an eight-yard touchdown toss from Manning four plays after an interception by linebacker Mike Peterson, who later left with a torn posterior cruciate ligament.
Chambers got loose for a 74-yard touchdown reception, giving Miami a 14-10 lead with just over 12 minutes left in the first half. Mare kicked the first of his two 31-yarders with 21 seconds left as the Dolphins took a 17-10 advantage to the locker room.
"It was a great read and a great throw," Chambers said. "I thought the ball would never come down."
Harrison caught touchdown passes of 11 and 40 yards less than five minutes apart in the third quarter, giving Indianapolis a 24-17 lead.
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