ORCHARD PARK, N.Y. (AP) Drake Maye threw three touchdown passes, including Efton Chism’s one-handed catch with 1:50 remaining, and the New England Patriots defeated the Buffalo Bills 29-26 on Sunday.

Romeo Doubs had touchdown catches of 2 and 14 yards, and Rhamondre Stevenson scored on a 1-yard run.

Though Maye’s turnover troubles continued with an interception and a lost fumble in the first half, the third-year starter was sharp in the final minutes after New England fell behind 26-21.

Maye’s 23-yard TD pass to Chism came on third-and-5, with the receiver bringing in the ball with his right hand and maintaining control in the end zone. Maye then hit Stevenson for the 2-point conversion.

Despite having a minute left and the ball at their 40, Josh Allen turned overly aggressive. On second-and-6, he spun out of Dre'Mont Jones' sack attempt, stepped up in the pocket and went deep only to have his underthrown pass intended for Josh Palmer intercepted by Craig Woodson.

Taking over at the Patriots 19, Maye put the finishing touches on the win by rolling to his right and lobbing a 12-yard pass to Hunter Henry in allowing the Patriots to run out the clock.

The Patriots improved to 2-2 and for once put aside questions about a sputtering and turnover-prone offense.

The Bills, meantime, dropped to 3-1 in Buffalo's first loss at its new Highmark Stadium, and first under new coach Joe Brady.

Maye finished 22 of 37 for 269 yards in overcoming the criticism he’s faced in opening the season by combining for six interceptions and a lost fumble in his first three starts. The lost fumble, recovered by the Buffalo at its 30, was on Maye, who lost the ball as Bills tackle Ed Oliver shoved an offensive lineman into him.

The interception, however, was on Doubs, who made the catch and in the process spun around and lost control of the ball, which sailed into the hands of cornerback Dee Alford.

The Bills had their sloppy moments, too, a week after committing five turnovers in a 24-16 win over the Los Angeles Chargers.

Receiver Khalil Shakir lost a fumble, in addition to Allen’s interception - his third of the season. Allen finished 23 of 33 for 253 yards, including a 34-yard go-ahead touchdown to Keon Coleman with 4:27 remaining. The touchdown put Buffalo up 26-21, but the 2-point conversion attempt failed when Palmer never looked for Allen’s pass directed his way.

Allen also scored on a 2-yard run, while James Cook scored on an 8-yard run.

The Bills were limited to 340 total yards and 19 first downs, both season lows, and resembled nothing like the high-powered unit that opened the season combining for 855 yards and 77 points.

The outing was a breakthrough for the Patriots’ slumbering offense, which posted season highs with 405 yards and 26 first downs. New England’s defense also rallied in containing the Bills despite missing its top cornerback Christian Gonzalez and starting defensive tackle Christian Barmore because of shoulder injuries.

Allen’s 2-yard touchdown run to tie the game at 14 with one minute left in the first half was his 88th career from scrimmage (rushing/receiving) to break the team record held by Hall of Famers Thurman Thomas and Andre Reed. It was also Allen’s 86th TD rushing, moving him into a tie with Priest Holmes for 16th place on the NFL's career list.

Patriots: WR Mack Hollins hurt his calf.

Bills: WR DJ Moore did not return after hurting his shoulder attempting to make a diving catch in the second quarter. DT Ed Oliver left in the third quarter with a knee injury. And a secondary already missing Christian Benford (toe), lost Dee Alford to an ankle injury in the second half.

Patriots: host the Las Vegas on Sunday.

Bills: at the Los Angeles Rams on "Monday Night Football" on Oct. 12

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