"We really haven't played good in the third quarter, but we did today," Patriots coach Bill Belichick said. "Things weren't going our way in the first half. That was obvious, being booed at halftime."
New England (6-2) rallied despite another mediocre performance by Brady, who completed more than half his passes for only the fifth time in eight games.
But his 116 yards passing were the second fewest in game he played most of the way in since 2006.
Brady completed 13 of 22 passes and threw a 14-yard touchdown pass to Aaron Dobson with 6:32 gone in the third quarter that began the comeback.
He threw for more than half his yards, 76, in the third quarter when the team scored 17 points. In their first seven games, the Patriots were outscored 44-9 in that period.
"I know a lot of people are frustrated," Brady said, but "to be 6-2 is not bad."
The Dolphins (3-4) lost their fourth straight game.
Trailing 17-3, New England got the ball for the second time in the third quarter after Caleb Sturgis' 46-yard field goal attempt hit the right upright.
"Maybe it changed momentum. Maybe it didn't," Miami quarterback Ryan Tannehill said. "That didn't matter. We needed to execute and needed to score points and we didn't."
The Patriots took over and scored on Brady's pass to Dobson.
They regained possession two plays after the kickoff when Logan Ryan sacked Tannehill, forcing a fumble that Rob Ninkovich recovered at the Miami 13. It was one of six sacks against Tannehill, who began the game having been sacked an NFL-high 26 times. Three plays later, Bolden scored on a 2-yard run.