In addition, Ryan Tannehill twice missed an open receiver deep.
"It's tough to beat a good team like New England with missed opportunities," guard Richie Incognito said. "We're a team with no margin for error. That's the story of the game they made their plays, and we didn't."
The Dolphins (5-7) hurt their already slim playoff chances and lost to New England for the fifth consecutive time.
"Too many mistakes," coach Joe Philbin said. "To beat a good opponent in December, you have to play better."
The Patriots (9-3) extended their winning streak to six games and are assured of their 12th winning season in a row. Afterward they wore championship caps and T-shirts.
"It's good to be back in the postseason," coach Bill Belichick said.
Brady finished 24 for 40 for 238 yards, was sacked four times and even threw an interception. But with the Patriots nursing a 20-13 lead midway through the fourth quarter, he led a 16-play drive that ate up more than seven minutes and led to a field goal.
Brady was intercepted for the first time in 203 passes, and for only the fourth time this season. His passer rating was a season-low 74.8, and he had at least four passes dropped, including a throw to Wes Welker in the end zone.
"It's not supposed to be easy, and it wasn't easy today," Brady said.
The Patriots kept their play-calling conservative and finished with a season-low 321 yards. But when they took over at their 20 leading by a touchdown in the fourth period, they produced their best drive of the day.
The 77-yard drive included 12 running plays and set up Gostkowski's field goal with 1:10 left. Stevan Ridley carried 10 times for 46 to spark the drive.
"We pounded away on a great defense, and they finally gave in a little," Ridley said.
Miami defensive ends Cameron Wake and Jared Odrick spent an extended time together on the sideline during the decisive drive. They declined to second-guess their coach.
"There was a different rotation this game, just the way we scheduled it," Odrick said.
Trevor Scott led New England's stout defensive effort with two sacks, including one to force a fumble that set up a field goal.
Jerod Mayo sacked Tannehill on third down midway through the fourth quarter, forcing the Dolphins to settle for a field goal.
Welker tied Jerry Rice's NFL record by making at least 10 receptions for the 17th time. He had 12 catches for 103 yards and a score.
Tannehill went only 13 for 29 for 186 yards, and twice he failed to connect with an open Brian Hartline deep.
"We just didn't hit the shots that were there," Tannehill said. "I'm still kicking myself."
Tannehill was most effective running the ball. He finished two keepers with brazen acrobatic leaps, vaulting over the goal line to elude linebacker Rob Ninkovich on a 2-yard touchdown run.
"You've got to battle; you're playing a good team," Tannehill said. "It's a game of inches, and you've got to do everything you can to get as many inches as you can."
The botched punt on the Dolphins' opening series led to a New England touchdown. With the ball wet following a brief shower, punter Brandon Fields dropped a low snap and was tackled at his 12. The Patriots scored five players later on Ridley's 2-yard run.
The roughing-the-punter penalty on Miami's Jimmy Wilson gave the Patriots a first down deep in their territory, jump-starting a 75-yard drive that ended with Welker's 7-yard touchdown catch.
Jones made a one-handed interception and returned the ball 30 yards for a touchdown, but the score was negated by a penalty on Reggie Bush for an illegal block. New England then held, and Dan Carpenter kicked a 44-yard field goal.
Notes: Dolphins T Jake Long left the game in the first half with a left triceps injury. ... Patriots G Dan Connolly left in the first quarter with a back injury. ... Dolphins reserve S Jonathon Amaya was inactive after being charged with battery Monday in a confrontation with a taxi driver.
New England 7 10 0 623
Miami 3 7 0 616
NE_Ridley 2 run (Gostkowski kick), 11:53.
Mia_FG Carpenter 44, :01.
NE_Welker 7 pass from Brady (Gostkowski kick), 9:21.
NE_FG Gostkowski 43, 6:53.
Mia_Tannehill 2 run (Carpenter kick), :25.
NE_FG Gostkowski 32, 13:16.
Mia_FG Carpenter 33, 8:28.
NE_FG Gostkowski 20, 1:10.
Mia_FG Carpenter 42, :31.
First downs 25 15
Total Net Yards 321 277
Rushes-yards 32-108 27-101
Passing 213 176
Punt Returns 2-25 2-7
Kickoff Returns 2-29 1-17
Interceptions Ret. 0-0 1-30
Comp-Att-Int 24-40-1 13-29-0
Sacked-Yards Lost 4-25 3-10
Punts 3-43.7 5-51.8
Fumbles-Lost 0-0 4-1
Penalties-Yards 6-50 8-92
Time of Possession 33:24 26:36
RUSHING_New England, Ridley 19-71, Woodhead 6-24, Vereen 3-14, Brady 4-(minus 1). Miami, Bush 15-64, Tannehill 5-19, Thomas 5-10, Thigpen 1-8, Fields 1-0.
PASSING_New England, Brady 24-40-1-238. Miami, Tannehill 13-29-0-186.
RECEIVING_New England, Welker 12-103, Hernandez 8-97, Woodhead 2-15, Edelman 1-13, Lloyd 1-10. Miami, Hartline 5-84, Clay 2-26, Thomas 2-19, Matthews 1-28, Fasano 1-14, Bess 1-13, Lane 1-2.
MISSED FIELD GOALS_New England, Gostkowski 49 (WR).