Derek Anderson and the Cleveland Browns get one more chance.

For Anderson, there’s another chance to show he deserves to remain the Browns’ starting quarterback. For Cleveland, there’s another chance to start living up to all of those high preseason expectations of winning the AFC North and making a deep run in the playoffs.

One chance, no more.

Anderson threw a fourth-quarter touchdown pass on Sunday for a 20-12 victory over the winless Cincinnati Bengals that provided a reprieve. A loss could have cost Anderson his job — he came close anyway — and would have left the Browns (1-3) in turmoil heading into their bye week.

Instead, they rallied to win an ugly game against a winless team that had lost its quarterback.

‘‘It almost put tears in my eyes to see us play as a team — a complete team,’’ receiver Joshua Cribbs said.

The Bengals? Forget it.

Carson Palmer sat out the game with a sore passing elbow, an injury left over from last week’s game. Without their offensive leader, the Bengals were totally out of sorts. Ryan Fitzpatrick threw three interceptions and ended up as Cincinnati’s leading rusher with 41 yards on scrambles.

The Bengals are off to their worst start in six years and their fourth 0-4 start since 1999. Next up is a game in Dallas, with the Cowboys coming off their first loss of the season.

Foreboding, huh?

‘‘It can’t get any worse than being 0-4 and playing the best team in the NFL,’’ receiver T.J. Houshmandzadeh said, referring to the Cowboys. ‘‘We’ve got to pick it up or we’ll get embarrassed. I would’ve bet the house on this game.’’

Given the way Anderson has played, all bets were off.

The Browns gave him a three-year, $24 million contract in the offseason, expecting him to lead the Browns to the playoffs after their near-miss last season. First-round draft pick Brady Quinn would watch from the sideline for another year.

After three poor performances by Anderson, coach Romeo Crennel was ready to make the switch if necessary. It might have happened, if not for a penalty.

The Browns were trailing 6-3 late in the third quarter when Anderson threw what would have been his second interception of the game. Fortunately for Anderson, it was nullified by an encroachment penalty on Cincinnati. At that point, Anderson was 7-for-15 for 53 yards, and Quinn was ready to go.

‘‘I decided to give him another chance,’’ Crennel said. ‘‘He went ahead and took advantage of it and finished on a good note.’’

Anderson’s 4-yard touchdown pass to Braylon Edwards put the Browns ahead to stay.

‘‘It said that he had faith in me to just keep doing it,’’ said Anderson, who finished 15-of-24 for 138 yards. ‘‘I’m never going to quit on him.’’

The question for the Bengals is how they’ll respond now that their season is in tatters along with their quarterback. Palmer has already had a broken nose, a sprained ankle, a bloody nose and an inflamed passing elbow.

He got his nose bloodied again in an overtime loss to the Giants a week ago, and hurt his elbow when he was hit while making a throw. The elbow then got worse as the week of practice went along.

On Saturday night, coach Marvin Lewis decided to make Palmer the emergency quarterback against Cleveland, letting him rest the elbow.

‘‘It’s not bad,’’ Palmer said. ‘‘I’ll probably be able to prepare this week.’’

The way things are going, he needs to be prepared for the worst.

‘‘This was a devastating loss for us in terms of dropping to 0-4 and going to Dallas next week,’’ Fitzpatrick said.

It was Cleveland’s first win since last Dec. 31. The Browns lost all four preseason games as well. … Edwards caught his first TD pass of the season. … The Bengals managed only 211 yards. It was the third consecutive game that the Browns’ defense held a team under 300 yards. … RB Jamal Lewis scored Cleveland’s first rushing touchdown of the season. He had 36 yards on the opening drive, only 43 the rest of the way. … Browns RT Kevin Shaffer left the game with a concussion. … Umpire Carl Paganelli got knocked down on a running play in the second quarter, his head hitting the ground hard. He later left with a slight concussion. … Cincinnati’s Chad Ocho Cinco caught a 4-yard touchdown pass, his first of the season. He didn’t celebrate.