The 42-year-old quarterback went 24-from-36 passes which included three touchdowns and 341 yards for the reigning Super Bowl champions, with Brady going to 6-0 in Massachusetts against the Steelers.
Pittsburgh quarterback Ben Roethlisberger had a less successful day, seemingly missing future hall-of-famer Antonio Brown who left the Pennsylvania franchise after last season.
The Patriots last week added Brown to their line-up after a short-lived spell with the Oakland Raiders.
Quarterback Nick Foles experienced a tough day at the office in his first season outing for the Jacksonville Jaguars since leaving the Philadelphia Eagles.
Kansas City Chiefs defensive tackle Chris Jones levelled the former Super Bowl MVP, fracturing the quarterback's clavicle after he threw a 35-yard touchdown pass to DJ Clark.
The 30-year-old will have surgery on Monday, with some league sources reporting the Jaguars may sign former San Francisco 49er Colin Kaepernick to cover the injury.
Kaepernick may be considered as an alternative backup Gardner Minshew, who threw two touchdowns and one interception as the Chiefs ran away 40-26 courtesy of reigning MVP Patrick Mahones.
The Los Angeles Rams scored an important 30-27 road victory over the Carolina Panthers, perennial strugglers the Cleveland Browns fell 43-13 to the Tennessee Titans and the Baltimore Ravens notched up the highest score of the day by going 59-10 over the Miami Marlins.
Kirk Cousins had a quiet night as he started his second season in Minnesota, attempting just 10 throws including eight successful ones for 98 yards and one touchdown.
The Vikings rush was the story of the night, churning through 174 yards on the way to a 28-12 victory over the Atlanta Falcons.
The Buffalo Bills finished 17-16 over the New York Jets, the Indianopolis Colts appeared to feel Andrew Luck's retirement as they went down 30-24 to the Los Angles Chargers and the Seattle Seahawks beat the Cincinnati Bengals 21-20.
The Detroit Tigers drew 27-all with the Arizona Cardinals, the Dallas Cowboys won 35-17 over the New York Giants, the 49ers took the Tamba Bay Bucanneers 31-17 and the Eagles opened the season 32-27 over the Washington Redskins.
The final game of the opening round will be the Houston Texans and the New Orleans Saints.