New England (9-2) posted its seventh consecutive victory and third straight win over Miami.
The Dolphins (4-7) have lost five straight for their longest slide since 2011.
It was Brady’s 28th career game with four or more touchdown passes — ranking third all-time. His 26 touchdowns passes are the most ever in a season after turning 40 years old.
Rex Burkhead also scored two TDs and Dion Lewis had 15 carries for 112 yards for New England, marking his first career 100-yard game. The Patriots went 5 for 5 in the red zone.
“We know our biggest games are ahead of us,” Brady said. “All the good teams are gonna start playing really well.”
Miami got within 28-17 in the fourth quarter, but came up empty on a fourth-down pass play with 8:48 left. On the ensuing series, the Patriots scored on a 5-yard touchdown pass from Brady to Brandin Cooks.
It was the 16th multi-touchdown game by Gronkowski, setting a franchise record. Randy Moss held the old record with 15.
The Dolphins played without quarterback Jay Cutler, who practised Friday, but remained in the concussion protocol.
The indomitable Philadelphia Eagles celebrated their ninth straight win in a 31-3 rout of the Chicago Bears that saw three touchdown passes for Carson Wentz.
Philadelphia now need to win just one game - and the Dallas Cowboys to lose to the Washington Redskins Thursday - to take the National Football Conference East division title and guarantee a spot in the play-offs.
Wentz passed for 227 yards, LeGarrette Blount rushed for 97, while Zach Ertz caught 10 over 103 yards.
Meanwhile, the Eagles’ defence made light work of Bears newcomer Mitchell Trubisky and kicker Cairo Santos missed a 54 yard field goal.
The Denver Broncos suffered a bruising 14-21 defeat to the Oakland Raiders in a game marred by a mass brawl.
Seemingly triggered by an altercation between Oakland receiver Michael Crabtree and Denver cornerback Aqib Talib, the fracas led to the pair being sent off, along with Raiders guard Gabe Jackson who pushed an official.
Oakland running back Marshawn Lynch sat as usual during the anthem, one of 23 NFL players who protested during Sunday’s games.
A last-gasp, personal record breaking 57-yard field goal by Phil Dawson lifted the Arizona Cardinals over the Jaguars 27-24 with one second to spare, ending Jacksonville’s four-game streak.
Meanwhile a final-minute field goal by Chris Boswell - a career best of 53 yards - saw the Pittsburgh Steelers edge the Green Bay Packers 31-28, their sixth straight win.
Jimmy Garoppolo made his debut for the 49ers with less than two minutes before the final whistle, finding Louis Murphy for a 10-yard touchdown, although it was far short of what San Francisco needed in the 24-13 loss to the Seattle Seahawks.
The Buffalo Bills closed out a slow-starting Kansas City Chiefs 16-10, their fifth loss in six games and the Indianapolis Colts lost 16-20 to the Tennessee Titans, the victors recovering from a seven-point deficit after half-time.
The Cincinnati Bengals extended the Cleveland Browns’ abysmal winless start to the season with a 30-16 drubbing. The Carolina Panthers made it four wins in a row with a 35-27 victory over the New York Jets, while the Los Angeles Rams ended the New Orleans Saints’ eight-game streak with a 26-20 win.