"We have a special team, a team with a lot of talent," receiver Brian Hartline said. "We're going to continue to improve. The sky's the limit."
An enthusiastic crowd of 70,660 reflected the buzz building about the surprising Dolphins, who are trying to end a streak of four consecutive losing seasons.
"We've got a damned good football team," owner Stephen Ross said. "The quarterback is maturing."
The last-minute comeback victory was the first for Miami's second-year QB. Tannehill finished 24 for 35 for 236 yards and two scores. He shook off two turnovers and five sacks, and was at his best at the end of each half.
On the final drive, Tannehill went 8 for 11 for 69 yards, with two of the incompletions because of dropped passes. The winner came on second down, when Tannehill lobbed his throw over linebacker Stephen Nicholas to Sims, a backup tight end.
Sims scored his first NFL touchdown by pulling the ball in with his left hand because his right arm was tangled up with Nicholas.
"It was awesome. It was amazing," Sims said. "The defender grabbed one hand, so I had no choice but to use the other one."
Tannehill suggested the play to his coaches during a timeout just beforehand.
"It's a play we know very well," he said. "It's either going to be a touchdown or a throwaway. We had a lot of confidence in that play."
Tannehill's other scoring pass was an 18-yarder to Hartline to make it 20-20 late in the third quarter. Tannehill also moved Miami 60 yards in the final 2:04 of the first half for a field goal on the final play.
The victory allowed Miami to keep pace with New England atop the AFC East.
"It was a good step forward," Hartline said. "Expectations will continue to rise, and high expectations bring out the best in you. We welcome it."
The Falcons believe they could be special, too, but they lost despite advantages of 24-16 in first downs, 377-285 in yards and 5-0 in sacks.
"It was a game where we had a ton of opportunities," coach Mike Smith said. "We need to be more efficient in the red zone on both sides of the ball. We had way too many field goals."
"Guys had to step up," said first-round draft pick Dion Jordan, who came off the bench to see his most extensive action of the season. "We stuck together and it came up big."
Ryan led drives of 14, 11 and 13 plays on the Falcons' first three possessions, but twice they stalled and settled for field goals.
"We had a lot of opportunities to finish the game," Ryan said. "We just didn't get it done in the red zone. We have to find a way to punch it in."
NOTES: The Dolphins have scored at least 20 points in each game, the first time they've done that since 2002. ... Atlanta's Matt Bosher, leading the league in punting, averaged 33.0 yards on two kicks. ... Osi Umenyiora had his first two sacks for Atlanta. ... Miami rookie Caleb Sturgis kicked field goals of 46 and 50 yards and is 6 for 6 this year.
Copyright 2013 by The Associated Press