CINCINNATI -- Cincinnati Bengals wide receiver A.J. Green shook his head and smiled when asked by a reporter if he had ever had a game like Sunday.

"That was a first," Green said, "and hopefully the last."

It wasn't pretty, but Green and the Bengals will take it.

Andy Dalton passed for 328 yards with a touchdown and two interceptions and Green had 189 receiving yards and a touchdown, lifting Cincinnati to a 20-16 victory over the Buffalo Bills at Paul Brown Stadium.

"I'm proud of them," said Bengals head coach Marvin Lewis. "We overcame a lot. They never stopped fighting."

Green dropped two passes that caromed into the arms of Bills' defenders, and he also lost a fumble. But the five-time Pro Bowler had a huge day on the stat sheet with seven catches and a 27-yard average.

"I hold myself to a high standard," Green said. "It's nothing on Andy (Dalton). Those were drops. I have to make those plays. That's on me."

Dalton injured his ankle during the second half and played with a noticeable limp. Backup AJ McCarron warmed up, but Dalton never left the game.

"I got it taped up, and it was good to go," Dalton said. "It got rolled at one point. It's fine. I'll be all right."

Tyrod Taylor was 20 of 37 for 166 yards with a touchdown and an interception for Buffalo (3-2), which missed a chance to go 4-1 for the first time since 2011.

Cincinnati (2-3) was the first team this season to score more than 17 points against the Bills.

Taylor was sacked six times.

"That's way too many," said Bills head coach Sean McDermott. "We've got to look at the film and do better there. Just trying to take what the defense was giving us. We obviously didn't make enough plays."

Remnants of Tropical Storm Nate resulted in soggy conditions throughout Sunday's game, and there were several dropped passes by both teams.

Buffalo had only allowed four touchdowns through four games, but the Bengals had some big plays against them on Sunday.

On the first play of the Bengals' second possession, Dalton connected with Green down the right sideline for a 77-yard touchdown pass to put them ahead 7-0. Green beat Buffalo cornerback Tre'Davious White for his third touchdown of the season.

"Any time you can get him one-on-one, it's a good thing," Dalton said.

Green had three catches for 99 yards and a touchdown on the first two possessions.

Cincinnati sacked Taylor twice in the first quarter, but he led the Bills on a 10-play, 72-yard drive that resulted in a 31-yard Stephen Hauschka field goal. It was the first points scored in the first quarter this season by Buffalo.

A roughing the passer penalty on Bills defensive end Jerry Hughes helped set up a 30-yard field goal by Randy Bullock to make the score 10-3.

Micah Hyde's fourth interception of the season on a tipped pass out of Green's hands set the Bills up at Cincinnati's 36-yard line.

"I told (Green), the good thing is, it goes on my stats, not his," Dalton said.

Brandon Tate, a former Bengal, caught a 12-yard pass for a touchdown to tie the score 10-10 with 3:10 left in the half. The drive was kept alive by Taylor, who scrambled away from pressure to complete a third-down pass.

Early in the second half, an interception by safety Jordan Poyer on a pass that went in and out of Green's hands gave the Bills possession at the Bengals' 36. However, a holding penalty moved Buffalo out of field-goal range, and the Bengals forced a punt.

Cincinnati's third turnover was a fumble by Green after a 20-yard completion, forced by a hard hit from linebacker Lorenzo Alexander and recovered by Poyer. That set up a 38-yard field goal by Hauschka to put Buffalo ahead 13-10 with 1:54 left in the third quarter.

"At the end of the day, when we create three turnovers, we have to find a way to get into the end zone, somehow, some way," Poyer said. "It's a tough loss."

Green redeemed himself with a 49-yard catch to set up running back Joe Mixon's first career touchdown run, giving the Bengals a 17-13 lead early in the fourth quarter.

Buffalo cut the lead to 17-16 on a 28-yard field goal set up by a 40-yard punt return by Tate. But again, three points, not seven.

"We've got to cash in on those situations," McDermott said. "We won the field position battle, and we didn't take advantage of it."

Bullock's 28-yard field goal with 3:33 left and safety George Iloka's interception of Taylor, the Bills' first turnover since their first possession of the season, sealed the win for Cincinnati.

"We didn't start the way we wanted to, but we earned that," Lewis said. "Now, we have to earn our way out of it. We took a step in the right direction."

NOTES: WR A.J. Green's 189 receiving yards for the Bengals are the most against the Bills since Wes Welker had 217 in 2011. ... Buffalo, already down to four healthy receivers, lost TE Charles Clay to a knee injury in the first half. ... Cincinnati lost CBs Adam Jones and Dre Kirkpatrick to injuries in the first half. ... Bills starting RG John Miller was a surprise healthy scratch. Vlad Ducasse started in his place. ... The Bengals have at least one sack in a league-leading 34 straight games.