The 41-year-old Brady completed 23 of 35 throws for 274 yards with three touchdowns and two interceptions as his side recovered from back-to-back losses.
Sony Michel rushed for 112 yards and a touchdown on 25 carries, becoming the first New England rookie to reach 100 rushing yards in a game in six years.
Brett Maher's last-gasp field goal handed the Dallas Cowboys a 26-24 victory over the Detroit Lions.
The Lions led with little more than two minutes remaining after Matthew Stafford found Golden Tate with a 38-yard touchdown pass.
But Dak Prescott guided the Cowboys on a nine-play, 55-yard drive to set up Maher's fourth field goal of the game from 38 yards.
Prescott completed 17 of 27 passes for 255 yards and two scores as running-back Ezekiel Elliott finished with a career-best 240 yards from scrimmage.
On a day of tight finishes, the Oakland Raiders needed overtime to beat the Cleveland Browns 45-42.
Nick Chubb's second touchdown on a 41-yard run gave Cleveland a 42-34 lead with just over four minutes remaining.
But Derek Carr threw to Jared Cook for a seven-yard score with 30 seconds left, and the Raiders quarterback then forced overtime with a two-point pass to Jordy Nelson.
Matt McCrane's overtime field goal then gave Jon Gruden his first victory on his return as Oakland coach.
There was also a 26-23 overtime win for Tennesse Titans over reigning Super Bowl champions the Philadelphia Eagles.
Marcus Mariota threw a 10-yard touchdown pass to Corey Davis with 17 seconds remaining in overtime to give the Titans a third straight win and inflict a second defeat on the Eagles.
The Los Angeles Chargers edged out the San Francisco 49ers 29-27 as Philip Rivers passed for 250 yards and three touchdowns.
The Cincinnati Bengals produced a thrilling finale to win 37-36 at the Atlanta Falcons and make it three wins in four games.
After a 75-yard drive, Andy Dalton hit AJ Green in the end zone for a 13-yard touchdown with seven seconds remaining.
The Baltimore Ravens' number one ranked defence set up a 26-14 victory over the Pittsburgh Steelers, whose typically explosive offence gave up two turnovers.
Ravens quarterback Joe Flacco passed for 363 yards and two touchdown and the reliable boot of Justin Tucker kicked four field goals.
The Green Bay Packers shut out the Buffalo Bills 22-0 as Aaron Rodgers threw for 298 yards and a touchdown.
The New Orleans Saints won 33-18 at the New York Giants with Alvin Kamara running in three touchdowns, while Sebastian Janikowski's 52-yard field goal saw the Seattle Seahawks scrape home 20-17 at the Arizona Cardinals.
Seattle suffered a blow, however, as six-time Pro Bowl free safety Earl Thomas suffered a broken leg and is expected to miss the rest of the season. Thomas, who has been in a contract dispute, appeared to make a crude gesture to the team's sideline as he was carted off.
The Chicago Bears thrashed the Tampa Bay Buccaneers 48-10 as Mitchell Trubisky enjoyed the best start of his two-year career.
Trubisky completed 19 of 26 passes for 354 yards, six touchdowns and no interceptions as the Bears secured a third win in four.
Ka'imi Fairbairn's 37-yard field goal halted the Houston Texans' nine-game winless streak as the Indianapolis Colts were beaten 37-34, while the Jacksonville Jaguars overwhelmed the New York Jets 31-12.