EAST RUTHERFORD, N.J. — Andy Dalton got hit hard by the New York Jets, early and often. In the end, the quarterback and the rest of the Cincinnati Bengals were the ones standing.

Mike Nugent kicked a 47-yard field goal with 54 seconds left, lifting the Bengals to a back-and-forth, 23-22 season-opening victory Sunday.

Dalton threw for 366 yards and a touchdown, but was sacked a career-high seven times.

The Jets’ Leonard Williams had 2½ sacks and Steve McLendon had two.

‘‘Any time you can get a win on the road, you’ve got to take these games,’’ Dalton said. ‘‘This one was big.’’

A.J. Green caught 12 passes for 180 yards, mostly against Darrelle Revis, to help the Bengals beat the Jets for the first time in 10 meetings in New Jersey.

‘‘The whole week everybody was saying A.J. vs. Darrelle,’’ Green said. ‘‘Revis is a first-ballot Hall of Famer. It’s my honor going against him. I was just trying to make plays any time the ball came my way.’’

Josh Shaw sealed the victory with an interception of Ryan Fitzpatrick in the closing seconds.

Cincinnati improved to 7-7 in openers under coach Marvin Lewis.

Nick Folk kicked a go-ahead 23-yard field goal with 3:23 remaining, but Dalton marched the Bengals downfield for the winning drive. The first missed extra point in Folk’s career and a blocked 22-yard field goal attempt came back to haunt the Jets.

Dalton finished 23 of 30 with the TD and an interception, and Jeremy Hill ran for 31 yards and a touchdown.

The Bengals took the lead in the third quarter when Hill bulldozed his way up the middle for a 12-yard TD. The drive was aided by Brandon LaFell’s 49-yard catch over Marcus Williams on third and 18.

The Jets drove to the Bengals 1 on their next possession, but stalled, leaving it to Folk to kick a 20-yard field goal to make it 20-19. After Nugent was wide right on a 52-yard attempt, the Jets drove down the field and went ahead on Folk’s 23-yarder.

Fitzpatrick finished 19 of 35 for 189 yards and TD passes to Quincy Enunwa and Eric Decker. The Jets were hurt by drives sputtering in the red zone and having to settle for field goal attempts rather than touchdowns.

‘‘We had our opportunities,’’ Fitzpatrick said. ‘‘We were winning in the fourth quarter and we just couldn’t shut the door.’’

Matt Forte, signed as a free agent in the offseason, ran for 96 yards on 22 carries and caught five passes for 59 yards in his Jets debut.