Chad Henne threw for a career-high 335 yards and directed a 51-yard drive for the winning field goal with 1:02 left.
"When you lose, it's an awful feeling," Brady said. "We're just not closing the game out when we have an opportunity."
AFC East leader New England (7-5) remained winless in five games in opponents' stadiums. For the third time on the road, the Patriots lost after leading in the fourth quarter.
"If things don't go your way, you've got to fight back," Brady said. "At times we do, and at other times I don't think we fight very hard."
The verdict was sealed when Channing Crowder made his first career interception, picking off Brady at the Patriots 40 with 35 seconds left.
Brady went to the locker room early in the game for treatment of an arm injury, but he returned without missing a play. He finished 19 for 29 for 352 yards and two long touchdowns, but he also threw two fourth-quarter interceptions, and New England scored only once in the final 44 minutes.
» The Patriots suffered their first defeat in their last eleven games following a loss.
Brady declined to blame his health, even though he came in with right shoulder and finger injuries.
"There are a lot of guys who are banged up," he said. "I don't think many guys are 100 percent. It's late in the year. It's a physical game. You've still got to go out and get the job done."
"Going against the top receivers week in and week out, you've got to grow up sometime," Davis said. "Today was one of those days to grow up."
New England subsequently forced Miami to punt twice, but each time Brady and the Patriots went three and out. On one play Brady overthrew an open Sam Aiken deep.
Brady threw touchdown passes of 58 yards to Moss and 81 yards to Aiken, and he also had a 58-yard completion to Wes Welker.
But New England twice failed to score inside the Miami 10. The Patriots were stopped on downs at the 6 in the second quarter.
"I have to coach better," coach Bill Belichick said. "We have to play better, just do a better job."
Welker had 10 receptions for 167 yards, but Moss was held to two catches.
"They're focusing a lot on him," Brady said. "You've got to get the ball to other guys when they do that."
Henne went 29 for 52 with one interception. It was the most passes thrown by the run-oriented Dolphins since 2006, and Henne endorsed Sparano's surprising game plan.
"If he wants to, we can throw all day," Henne said. "I love it. Put it in my hands in pressure situations."
Brady hurt his arm taking a hit as he threw the touchdown bomb to Moss on the opening series. While the Patriots celebrated, their quarterback trotted off the field and kept going, vanishing through the tunnel.
He returned five minutes later, and following a Miami punt he was back in the game to direct a 13-play, 80-yard drive for a 14-0 lead.
"You have to be mentally tough to win on the road," Patriots safety Brandon Meriweather said. "Right now, our team isn't mentally tough like it's supposed to be."
Notes: For the first time this season, Miami didn't run a wildcat play. ... Broadcaster Larry King joined the Dolphins' radio team for part of the game. King did color commentary for the Dolphins in 1969-71 and in 1977. ... Miami's Davone Bess had 10 catches for 117 yards, both career highs. ... In the past nine games, Brady has thrown only one fourth-quarter touchdown pass.
Copyright 2009 by The Associated Press