Brady completed 29-of-35 passes for 376 yards as host New England downed Cincinnati 35-17.
New England Patriots star Tom Brady and Dallas Cowboys rookie Dak Prescott each threw three touchdown passes to spark NFL triumphs that boosted each club to 5-1.
Brady completed 29-of-35 passes for 376 yards as host New England downed Cincinnati 35-17, while Prescott went 18-of-27 for 247 yards as Dallas won 30-16 at Green Bay.
The only NFL club with a better record, the 5-0 Minnesota Vikings, had a bye week. They play again next Sunday at Philadelphia.
Brady tossed two touchdown passes to James White and another to Rob Gronkowski to surpass the career 5,000-completion mark as the 39-year-old, four-time Super Bowl champion improved to 49-1 in regular-season home games over the past decade.
"It's good to be 5-1. I think we're in a decent place," said Brady, playing his second game of the season after serving his four-game Deflategate ban. "I could do some things better out there and I think offensively we can too."
Gronkowski, who missed practice Friday due to illness, caught seven passes for a career-high 162 yards while White caught eight for 47 yards.
Prescott broke Brady's NFL record for most pass attempts to start a career without an interception with his 163rd throw, but the newcomer who has replaced injured Tony Romo saw his streak snapped at 176 when he was picked off by Green Bay's Morgan Burnett.
Romo returns in two weeks but might not unseat Prescott as a starter.
"That's up to the coaches," Prescott said. "I just come in here and work my butt off and try my best to get my team to win."
Oakland and Atlanta failed to reach 5-1 with losses Sunday, NFL defensive leader Seattle edging league scoring leaders Atlanta 26-24 while Kansas City ripped Oakland 26-10.
"We got outcoached and outplayed. Take your pick," Raiders coach Jack Del Rio said.
Eli Manning threw for 403 yards and three touchdown passes to spark the New York Giants over visiting Baltimore 27-23.
Odell Beckham Jr. made eight catches for 222 yards, the second-most in a game in Giants history, with touchdown receptions of 75 and 66 yards.
The Giants visit London next Sunday for a Twickenham date with the Los Angeles Rams, who lost 31-28 to Detroit as Matthew Stafford threw for 270 yards and four touchdowns.
Rookie Wil Lutz kicked a 52-yard field goal with 11 seconds remaining to give New Orleans a 41-38 victory over Carolina. Saints quarterback Drew Brees threw for 465 yards and four touchdowns, setting an NFL record with his 15th 400-yard passing performance.
Jay Ajayi ran for a career-high 204 yards and scored two touchdowns to power Miami to a 30-15 upset of visiting Pittsburgh.
The defeat could prove especially costly to the Steelers, whose quarterback Ben Roethlisberger suffered a left knee injury in the second quarter. He returned to the game, but looked nothing like the QB who came into the contest averaging 299.2 passing yards per game and was reported by US media to be facing surgery for a torn meniscus.
LeSean McCoy rushed for 140 yards and three touchdowns as Buffalo ripped San Francisco 45-16, the Bills achieving a four-game win streak for the first time in eight years.
Washington also won a fourth consecutive game as Kirk Cousins threw for two touchdowns in a 27-20 victory over the Philadelphia Eagles.
Arrelious Benn caught a 51-yard touchdown pass from Blake Bortles with 2:49 remaining to give Jacksonville a 17-16 comeback victory at Chicago.
In Houston, the Texans erased a 14-point fourth-quarter deficit to beat the Indianapolis Colts 26-23 in overtime, with Nick Novak delivering the game-winning 33-yard field goal.
The Browns, the only winless NFL team at 0-6, and Eagles used tiny electric gridiron game figures to simulate actual contest highlights in Twitter posts, poking fun at new NFL rules preventing teams from using game video on social media.
The social media rules and a crackdown on post-touchdown celebration antics has renewed criticism of the NFL as the No Fun League.