ORCHARD PARK, N.Y. -- After the New York Jets claimed their first road victory of the season, against the former coach they couldn't beat last year, the familiar chant rang out from the visitor's locker room, "And the home of the Jets!"

Matt Forte rushed for 100 yards and three touchdowns, Ryan Fitzpatrick threw for 374 yards and a touchdown, and the Jets beat the Buffalo Bills 37-31 on Thursday night at New Era Field.

New York (1-1) bounced back from a last-minute loss in the opener at Cincinnati on Sunday.

Winning in upstate New York for the first time since 2011 -- when Fitzpatrick was the Bills' quarterback and current Buffalo coach Rex Ryan was still commanding the Jets -- avenged a loss in last season's finale that kept the Jets out of the playoffs.

"It was a big game," said Forte, who joined the Jets in free agency. "Coming back after a close game last week, to come back and get a win here in a hostile environment against a division rival is huge. It was a must-win."

Forte finished off the Bills with a 12-yard touchdown run that gave the Jets a 13-point lead with 4:02 remaining. His 3-yard touchdown run in the third quarter put the Jets in front 27-24. He also scored on a 1-yard plunge early in the second quarter.

However, it was Fitzpatrick who led the Jets' 493-yard, 28-first down output, their best performance in the 18 games he has been under center.

Fitzpatrick completed 24 of 34 passes, and his passing-yardage total was the fourth highest of his career. He also didn't throw an interception after throwing three in last season's loss at Buffalo.

"He was on the money," New York receiver Brandon Marshall said.

Coming into the game, Fitzpatrick had a 2-8 record against Rex Ryan as a starter, averaging 165 yards in those contests, with 16 touchdowns and 12 picks.

"He's played well in other games," Jets coach Todd Bowles said. "But against this team, this was the best we've seen him."

Fitzpatrick completed six passes each to receivers Eric Decker (126 yards, one touchdown), Marshall (101 yards), and Quincy Enunwa (92 yards).

"Our big-time players made some big-time plays," Bowles said.

Buffalo quarterback Tyrod Taylor passed for a career-high 297 yards and three touchdowns but also threw a fourth-quarter interception as the Bills fell to 0-2 for the first time since 2010, when they lost the first eight games.

After allowing only 13 points and 308 yards in last week's loss at Baltimore, the Bills' defense continued the inconsistency it displayed in Ryan's first season as coach.

"We had a rough day, there's no question about it," Ryan said. "I thought we played well defensively the first game. We played, I mean, horribly today."

After generating only 160 yards in the opener, the Bills' offense bounced back to rack up 393 yards. However, 155 of those yards came on two plays. Ryan said he wasn't concerned about the offense.

"To be honest with you, I think our defense played so poorly that I couldn't tell you about that," Ryan said.

The Bills got within a touchdown on Mike Gillislee's 18-yard touchdown catch of a Taylor pass with 1:17 left in the game.

Marshall recovered the Bills' onside kick attempt, and the Forte ran the clock down to 10 seconds before the Bills got the ball back one final time. A hook-and-ladder pass got the Bills near midfield, but lacking any timeouts, they could not run another play.

New York kicker Nick Folk's third field goal of the game, from 36 yards out, made it 30-24 with 10:40 remaining.

The Bills scored two touchdowns in the first 3:32 of the second half to take a 24-20 lead.

On the third play of the third quarter, Taylor rolled to his right to escape the rush and located a wide-open Greg Salas for a 71-yard touchdown pass.

Five plays into the Jets' ensuing drive, Bills linebacker Preston Brown punched the ball free from Jets receiver Jalin Marshall, and cornerback Nickell Robey-Coleman returned the recovered fumble 36 yards for the go-ahead score.

Dan Carpenter's 38-yard field goal cut the Jets' lead to 20-10 just before halftime.

New York scored on each of its first four drives in building a 20-7 lead.

The Jets possessed the ball for 13:35 of the first quarter, taking an early lead on a 28-yard Folk field goal, then making it 7-6 on Folk's 29-yarder on the final play of the quarter.

Marquise Goodwin sprinted past Darrelle Revis down the right sideline to haul in an 84-yard touchdown pass from Taylor and vault the Bills in front 7-3 on just their second offensive play.

NOTES: Jets WR Brandon Marshall twisted his left knee when Bills CB Stephon Gilmore grabbed his facemask on a second-quarter reception. Marshall went to the locker room to be evaluated but returned to the game on the next series. Jets LG James Carpenter also injured his calf on the same play. ... Jets rookie OLB Jordan Jenkins (calf) did not play. ... LT Cordy Glenn (ankle) sat for the Bills. WR Sammy Watkins (foot) and TE Charles Clay (knee) both started after being listed as questionable. ... The Bills retired the No. 78 jersey number worn by Hall of Famer Bruce Smith, the NFL's all-time sack leader, during a halftime ceremony. ... Darius Rucker, a country singer and former lead singer of the band Hootie and the Blowfish, performed the national anthem, at Smith's request.