Brady passed for 340 yards and a touchdown and ran for another score, diving head-first between two defenders in a rare run by the 41-year-old quarterback.
"I got close to the goal line and I just figured I'd try to get it in," Brady said of his late TD plunge. "We needed it."
New England's third straight win was Brady's 200th victory as a starting QB, tops all-time. He also passed former teammate Adam Vinatieri for most career wins in the regular season and playoffs combined with 227.
Brady got some help from rookie Sony Michel, who rushed 24 times for 106 yards and two touchdowns in another solid performance.
"It's tough to slow those guys down, they've been scoring a lot of points all year," Brady said. "They're gonna be pretty tough to stop. Glad we had our last shot and glad we took advantage of it."
It was the first loss of the season for the Chiefs (5-1), who were again let down by a defense that came in allowing an NFL-worst 462 yards per game.
New England (4-2) led 24-9 at intermission, but Mahomes directed an impressive rally for Kansas City. He finished 23 of 36 for 352 yards in his first loss as a starting quarterback, with three of his four TD passes going to Tyreek Hill.
Mahomes threw two interceptions in the first half but was unflappable down the stretch. He found Hill for a 1-yard TD pass that made it 33-30 Kansas City with 8:38 left. With the Chiefs trailing 40-33, he connected with Hill again for a 75-yard score that tied the game with just over three minutes remaining.
"The last two weeks it seems like we just can't punch it in there and I feel like the second half we finally started getting it in the end zone," Mahomes said.
After electrifying the NFL during the first five weeks of the season with his freewheeling style and big arm, Mahomes looked unsure of himself early on.
He was able to complete some long passes to get the Chiefs into the red zone. But he turned the ball over twice in the first half and the high-scoring Chiefs were held to three field goals.
Everything changed in the second half.
First, Mahomes broke through with a 67-yard touchdown pass to Kareem Hunt . That was followed by a 14-yard TD strike to Hill that came on the heels of a fumble by Brady, helping trim New England's lead to 27-26 entering the fourth quarter.
A 39-yard field goal by Gostkowski stretched New England's lead to 30-26.
But Kansas City kept coming.
Tremon Smith took the ensuing kickoff 97 yards down the sideline to the Patriots 3, setting up Hill's go-ahead TD.
The Patriots responded, using 42-yard pass from Brady to Chris Hogan to help set up a 4-yard touchdown run by Brady that put the Patriots back in front.
Then, after forcing Kansas City into the first punt by either team on the night, Brady got the Patriots some breathing room when he hit Gronkowski for a 42-yard gain. The play set up 50-yard field goal by Gostkowski.
The Chiefs also started 5-0 last season before losing six of their last 11 and falling in the wild-card round of the playoffs.
But coach Andy Reid said he is confident his team has room to grow.
"We will learn a lot from this game," he said. "We kind of shot ourselves in the foot a little bit early and you can't do that against a good football team."
The Chiefs extended their streak for scoring on their first possession in every game this season.
Harrison Butker connected on a 42-yard field goal with 9:05 left in the first quarter, capping an eight-play, 35-yard drive that began after the Patriots turned it over on downs.
PICKING IT OFF
The Patriots now have at least one interception in each of their first six games of the season. New England's last streak of six consecutive games with an INT was in 2013.
EDELMAN ENDS DROUGHT
New England's Julian Edelman caught a 17-yard touchdown pass in the second quarter , his first since January 22, 2017, in the AFC championship game against the Steelers
In those 630 days, including the playoffs, Brady threw 54 touchdown passes to 11 different players.
Edelman sat out the entire 2017 season after suffering a preseason knee injury. He missed the first four games this season while serving a suspension for violating the NFL's policy on performance enhancers.
Chiefs: C Mitch Morse was evaluated for concussion in the second quarter and did not return.
Patriots: Right tackle Marcus Cannon left in the second half with a head injury and did not return.
The Chiefs return home to host Cincinnati.
The Patriots go on the road for the third time this season when they visit the Bears.
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Von Miller says that the Broncos were lacking confidence and hoped his message would help, and wants to keep the same mentality each week.
Josh Rosen talks about left his toe injury and how he can bounce back next game after a tough loss to the Broncos.
Steve Wilks reflects on Thursday night's blowout loss to the Broncos and Josh Rosen's injury status.
Emmanuel Sanders gets the ball on a reverse and throws a deep ball to Courtland Sutton for a 28-yard score.
Cardinals coach Steve Wilks acknowledged that rookie quarterback Josh Rosen probably shouldn't have been in the game late in the fourth quarter of Thursday's blowout loss to the Broncos, when he suffered a left toe injury.
Changes could be made, as the Cardinals' offense continues to sputter versus the Broncos.