The loss eliminated the Falcons (7-8) from the playoffs and clinched the third and final NFC wild card berth for the Tampa Bay Buccaneers.
The Dolphins (10-5), the only team to make the playoffs in each of the last five years, moved into a tie for first place with New England (10-5) in the AFC East. But the Patriots have the tiebreaker advantage on the basis of a better division record.
Miami finishes the regular season at home next weekend against Buffalo while the Patriots visit Carolina, which has lost 14 in a row.
"This gives us 10 wins and we're going to appreciate what this means -- 10 wins and we're in the playoffs," Dolphins Coach Dave Wannstedt said.
The Dolphins forced four turnovers and have 25 takeways in their 10 wins and zero takeaways in their five losses.
Atlanta had a chance to tie the game with a third and goal at the one inside the two-minute mark. But fullback Bob Christian was stuffed for no gain on two straight runs, although the Falcons thought Christian broke the plane of the goal line on the first one.
Running behind left guard, Christian appeared to sneak the ball over the goal line after he was tackled by end Kenny Mixon and linebacker Zach Thomas. But no touchdown was signaled and a replay challenge upheld the call.
"I asked (referee) Bernie Kukar and he told me there was no question the ball crossed the plane of the goal line, but he couldn't tell if the knee was down," Falcons coach Dan Reeves said. "I said if the ball breaks the plane, I don't know how you can't call it a touchdown."
There was no doubt that Christian did not get into the end zone on the next play. Instead of trying a rollout with rookie quarterback Michael Vick, the Falcons opted for the same play with Christian running behind left guard and he was knocked back by Thomas and defensive tackle Ernest Grant for no gain with 47 seconds remaining.
"I thought Vick was going to have the ball in his hands," Taylor said of Atlanta's fourth-down call. I was surprised. They ran the ball into the heart of our defense."
It was the second goal-line stand of the day for the Dolphins. Thomas stopped Falcons back Maurice Smith for no gain on fourth and goal at the one with 3:31 left in the third quarter.
"I don't know if I have been involved in a game with two goal-line stands before," Wannstedt said. "That was just a phenomenal effort by our entire defense."
"Our defensive line did a great job," said Thomas, who finished with 14 tackles and two sacks. "I was running free all day."
Vick replaced starter Chris Chandler, who injured his left elbow late in the first half, and threw for 214 yards, including a one-yard touchdown to tight end Derek Rackley, and ran for 63 yards on five scrambles.
"You've got to give Michael Vick credit," Wannstedt said. "Obviously, he's going to be a heckuva player."
"He (Vick) has unbelievable abilities, you can see that," Reeves said of the player he selected with the first pick in the draft. He can run the football and make great throws, but as a young quarterback he's going to turn it over. I thought he made some plays that were really unique as far as talent is concerned."
Miami's Jay Fiedler was 16 of 29 for 191 yards and two touchdowns with one interception. The maligned quarterback has passed for 3,180 yards this season.
However, Fiedler's first pass of the game was deflected by linebacker Keith Brooking and intercepted by cornerback Ray Buchanan, who returned it 29 yards to the Miami 29. Smith gained 16 yards on a sweep to his left to the 13 and scored on a two-yard run with 9:02 left in the quarter, giving Atlanta a 7-0 lead.
The Falcons had a chance to increase their lead to 10-0 but Jay Feely had a 44-yard field goal attempt blocked by Mixon.
Meanwhile, Miami's offense totaled minus-seven yards on their first four possessions with three three-and-outs following the interception.
But the defense came to the rescue when Marion raced in from his free safety position to pick off a pass intended for former Dolphin Tony Martin and returned it 26 yards for a touchdown with 59 seconds left in the quarter.
Chandler completed seven of 11 passes for 51 yards before he injured his right elbow after getting hit by blitzing safety Arturo Freeman with 5:19 left in the second quarter. He was replaced by Vick and did not return.
The Dolphins scored two touchdowns in a 54-second span late in the half. Rookie Travis Minor caught a screen pass from Fiedler and turned it into a 17-yard touchdown with 1:02 left in the half, capping a nine-play, 67-yard drive.
"That was a set up screen pass," Fiedler said. "The end was rushing wide upfield. Travis just turned it around."
Fiedler hit James McKnight with a 14-yard pass and scrambled for a 13-yard run on third-down plays to keep the drive alive.
Miami's defense set up Miami's final touchdown when end Lorenzo Bromell sacked Vick, forced a fumble and Taylor recovered at the Atlanta 33 and returned it three yards with 39 seconds left in the half.
Fiedler hit Oronde Gadsden with an eight-yard pass and Minor went off right tackle for 11 yards to the Atlanta 11.
After calling a timeout with 20 seconds left, Fiedler threw a nine-yard pass to rookie Chris Chambers and hit Gadsden with a two-yard touchdown with eight seconds left in the half, giving Miami a 21-7 lead.
Cornerback Patrick Surtain intercepted a pass by Vick at the Miami 28 early in the third quarter and the Dolphins came through with their first goal-line stand later in the quarter after Vick hit Brian Finneran with a 52-yard pass to the Miami four.
The Falcons pulled within 21-14 when Vick rolled to his left and hit Rackley in the back of the end zone after connecting with Shawn Jefferson on a 48-yard bomb.
Swim Week Miami Beach 2014 [PHOTOS]