Gronkowski reeled in seven catches for 123 yards and a touchdown. Brady, 41, completed 26-of-39 passes while also throwing one interception to go with his three scores.
"All that talk about that stuff, I would love to put it in the past," Gronkowski told reporters. "I'm here. I'm here to stay. I'm enjoying my time."
Texans quarterback Deshaun Watson, who suffered a torn ACL last season that resulted in him missing the final nine games of the year, completed 17-of-34 passes for 176 yards with one touchdown and an interception.
Texans wide receiver DeAndre Hopkins recorded eight receptions for 78 yards in his return to action with Watson under center. Bruce Ellington had four catches and 37 yards with a touchdown.
It's not a win, but it's also not a loss for the Cleveland Browns, who had gone a combined 1-31 in the last two seasons.
In a rain-filled contest, quarterback Ben Roethlisberger and the Steelers turned the ball over six times. Roethlisberger completed 23-of-41 pass attempts for 335 yards with one touchdown and three picks.
Browns quarterback Tyrod Taylor, making his Cleveland debut, was 15-for-40 with 197 passing yards, one touchdown and one pick. He had eight rushes for 77 yards and another score.
Both teams had field goal chances in overtime to win the game, but could not convert the opportunities.
The Bengals spoiled the return of Colts quarterback Andrew Luck, who hadn't played in the previous 20 months while rehabbing from a major shoulder injury.
Cincinnati signal-caller Andy Dalton completed 21-of-28 pass attempts for 243 yards with two touchdowns and one interception. Bengals running back Joe Mixon carried the ball 17 times for 95 yards and a score.
In his return, Luck was 39-of-53 with 319 yards, two touchdowns and one pick.
Giants rookie running back Saquon Barkley shined in his debut, but New York couldn't find enough offense to counter the Jaguars' stout defense.
Barkley had 18 rushes for 106 yards with a touchdown. The score came on a 68-yard run that saw the Penn State product evade multiple defenders while tip-toeing down the sideline.
Jacksonville linebacker Myles Jack's 32-yard touchdown off an interception return proved to be the game-winning score.
Odell Beckham Jr. returned from his ankle injury to post 11 receptions and 111 yards.
In an NFC South shootout, Tampa Bay quarterback Ryan Fitzpatrick and the Buccaneers stunned the 2017 division champions.
Fitzpatrick completed 21-of-28 attempts for 417 yards and four touchdowns. The veteran quarterback also ran 12 times for 36 yards and another score.
Minnesota quarterback Kirk Cousins made his much-anticipated debut with the Vikings. In his first start with the club, he passed for 244 yards and two touchdowns.
Vikings running back Dalvin Cook, making his return from a torn ACL sustained early last season, had a fairly substantial workload. He had a team-high 16 carries for 40 yards, and added six catches for 55 yards.
49ers quarterback Jimmy Garoppolo struggled in the season opener, completing 15-of-33 passes for 261 yards, one touchdown and three interceptions.
Joe Flacco and the Ravens cruised to an easy victory over Nathan Peterman and the sluggish Bills Sunday afternoon.
Flacco went 25-of-34 for 236 yards and three touchdowns before being replaced by rookie Lamar Jackson in the third quarter.
The Ravens, under new defensive coordinator Don Martindale, held Buffalo to 33 yards and no first downs in the first half of play.
Peterman was 5-for-18 with 24 yards and two interceptions before being benched for rookie first-rounder Josh Allen. Allen completed 6-of-15 passes for 74 yards with no touchdowns or picks in his debut.
The Dolphins outlasted the Titans in the longest game since the 1970 NFL-AFL merger. Multiple lightning delays pushed the contest's ending back.
The previous record was held by the Chicago Bears and Baltimore Ravens, who survived a five-hour, 16-minute marathon on Nov. 17, 2013.
Titans quarterback Marcus Mariota threw two interceptions in the third quarter, eventually leaving the game with an elbow injury. He finished the day 9-for-16 passing with 103 yards and two picks.
Blaine Gabbert replaced the injured Mariota and completed 11-of-22 passes for 117 yards and an interception.
Tennessee offensive lineman Taylor Lewan (concussion) and tight end Delanie Walker, who was carted off the field with a right leg injury, also exited the contest and both did not return.
Dolphins quarterback Ryan Tannehill, playing in his first game since a knee injury in late 2016, went 20-for-28 with two touchdowns and two picks. He added four carries for four yards.
Kansas City Chiefs 38, Los Angeles Chargers 28
Chiefs receiver Tyreek Hill established a quick rapport with young gunslinger Patrick Mahomes, grabbing seven catches for 169 yards and two touchdowns. Hill added another score on a 91-yard punt return.
Mahomes was 15-for-27 with 256 yards and four touchdowns.
Chargers veteran Philip Rivers completed 34-of-51 passes for 424 yards, three touchdowns and one interception.
Broncos newcomer Case Keenum had some bright spots and a few miscues, but managed to guide his new club to a slim victory over the Seahawks.
Keenum was 25-of-39 with 329 passing yards and three touchdowns, but also tossed three interceptions. Emmanuel Sanders was his favorite target on the day, recording 10 receptions for 135 yards and a score.
Seahawks quarterback Russell Wilson completed 19-of-33 throws for 298 yards, three scores and two picks.
Panthers dual-threat quarterback Cam Newton displayed his full skillset against the Cowboys, throwing for 161 yards (17-of-26 passing) while rushing 13 times for 58 yards and a touchdown.
Cowboys third-year quarterback Dak Prescott struggled behind an offensive line that allowed six sacks late Sunday afternoon. He completed 19-of-29 passes for 170 yards.
Dallas running back Ezekiel Elliott ran 15 times for 69 yards and a touchdown, and added three receptions for 17 yards.
Smith was 21-of-30 passing for 255 yards and two touchdowns. He also had eight carries for 14 yards.
Fellow newcomer Adrian Peterson saw a heavy workload in his first game with Washington, rushing 26 times for 96 yards and a score. The former NFL MVP added two catches for a team-high 70 yards.
Bradford completed 20-of-34 passes with 153 yards and one interception. David Johnson ran nine times for 37 yards and a touchdown in his return from a season-ending wrist injury.