CLEVELAND — Marvin Lewis wanted to play it safe. The Cincinnati Bengals wanted more.

‘‘We came here to play for a win,’’ Carson Palmer said. ‘‘Nothing else.’’

These Bengals have lost long enough.

After Palmer and his teammates convinced their coach to gamble on fourth-and-11 with just over one minute left, Palmer scrambled for 15 yards to set up Shayne Graham’s 31-yard field goal on the final play of overtime, giving Cincinnati a 23-20 victory over the winless Cleveland Browns on Sunday.

The last-minute Bengals (3-1), whose four games have all gone down to the wire, faced a fourth-and 11 at Cleveland’s 41 with 1:04 left. Lewis was content to play for the tie, but when the Browns called a timeout, it gave the Bengals a chance to lobby their coach.

They made a persuasive argument.

Palmer dropped back to pass, and seeing his receivers were covered downfield, tucked it away and ran up the middle for the first down. Cincinnati then ran two plays to get Graham in position, and the kicker, who had an extra point and field goal blocked by nose tackle Shaun Rogers, booted the winner.

‘‘Marvin was saying we’re going to punt,’’ Palmer said of his sideline negotiation with Lewis. ‘‘I said I think we can get this. That’s why Marvin’s great. He listens to people around him. Most coaches, once they make up their mind, they make up their mind.

‘‘That’s why you love playing for a guy like Marvin. Your opinion does matter.’’

Defensive end Robert Geathers returned a fumble 75 yards for a TD for Cincinnati, which is tied with Baltimore for first in the AFC North. The Bengals visit the Ravens next Sunday.

After three lopsided losses under first-year coach Eric Mangini, the Browns (0-4) came in hoping to be competitive and were that and more. They outplayed the Bengals for three quarters but came up short and had their losing streak extended to 10 games dating to last season.

‘‘Nobody’s happy,’’ said quarterback Derek Anderson, who provided a huge spark in his first start this season. ‘‘We lost. Nobody’s happy we went to overtime and played it to the last 10 seconds. That’s not what we’re here for.’’

Palmer, who rallied the Bengals to a comeback win over the Super Bowl champion Steelers last week, finished 23 of 44 for 230 yards. He threw two TD passes to Chad Ochocinco, who only had three catches but made the most of them.

‘‘The whole thing keeping me going is No. 9,’’ Ochocinco said of Palmer, who missed 12 games last season with an elbow injury. ‘‘He’s so confident in the huddle. The way he has been the last two weeks is unbelievable. Especially the situations we’ve been in.’’

Browns running back Jerome Harrison, filling in for the injured Jamal Lewis, had 121 yards on 29 tries. Joshua Cribbs had 223 return yards, but couldn’t do enough to end Cleveland’s losing slide.

‘‘There’s no sugarcoating it,’’ wide receiver Braylon Edwards said. ‘‘You can say it’s something to build on, but it hurts. To have the wind knocked out of you at the end, it definitely hurts.’’

Just like last week, Palmer was at his best with the stakes at their highest.

He completed two third-and-10 passes on Cincinnati’s final drive, hooking up on a 20-yarder to Chris Henry over the middle and then another one to Laveranues Coles. But it was his decision to take off and run for the game’s biggest first down that will be remembered.

If that play had backfired, the Browns would have gotten the ball back near midfield with a chance to win and Lewis, who has the Bengals off to their best start since 2006, would have been second-guessed for weeks.

‘‘It’s a great call because we had nothing to lose,’’ running back Cedric Benson said. ‘‘It’s either a tie or a loss, and a tie is pretty much a loss anyway.’’

On his clutch run, Palmer ran as far as he needed and plopped down.

‘‘I don’t want to do that anymore,’’ he joked. ‘‘Let Cedric do that.’’

Anderson, making his first start since Mangini benched Brady Quinn, completed 26 of 48 passes for 269 yards, threw a 2-yard TD pass to Steve Heiden and ran for a score. Rookie Mohamed Massaquoi had eight catches for 148 yards.

As usual Anderson had some bad moments. He threw an interception in the end zone with the Browns down 14-7, but later atoned for it with his TD run that tied it 14-all.

‘‘I was really happy with him,’’ Mangini said of Anderson. ‘‘He made a lot of nice throws.’’

The Bengals did nothing on offense for three quarters and then suddenly awakened with a possible loss looming.

After gaining 156 yards in the first quarter, Cincinnati went seven straight possessions without picking up a first down and the Bengals found themselves trailing 20-14. Palmer then drove for what looked to be a go-ahead score when he hit Ochocinco from 2 yards with 1:55 left to tie it 20-20.

The Bengals were seemingly on the verge of another dramatic win, but Graham’s extra point was blocked by Rogers, who deflected a 23-yard field goal attempt in the first.

Cincinnati was forced into overtime, continuing a run of nail-biters Palmer would like to see end soon.

‘‘It’d be nice to go up by a couple scores and drink some Gatorade as we take a knee at the end,’’ he said.

NOTES: Browns WR Mike Furrey played both ways, including safety in certain defensive packages. … Edwards did not have a reception for the first time in 62 career games. … The Bengals narrowly avoided their second tie in two seasons. They played Philadelphia to a 13-13 draw on Nov. 16. … Rogers has 13 career blocked field goals and two blocked PATs.

Cincinnati 7 7 0 6 3 — 23

Cleveland 0 7 7 6 0 — 20

First Quarter

Cin—Ochocinco 5 pass from C.Palmer (Graham kick), :35.

Second Quarter

Cin—Geathers 75 fumble return (Graham kick), 14:10.

Cle—Heiden 1 pass from Anderson (Cundiff kick), 1:26.

Third Quarter

Cle—Anderson 1 run (Cundiff kick), 1:37.

Fourth Quarter

Cle—FG Cundiff 26, 14:58.

Cle—FG Cundiff 31, 6:34.

Cin—Ochocinco 2 pass from C.Palmer (kick blocked), 1:55.

Overtime

Cin—FG Graham 31, :07.

A—69,844.

———

Cin Cle

First downs 21 22

Total Net Yards 375 395

Rushes-yards 30-154 33-146

Passing 221 249

Punt Returns 3-17 6-120

Kickoff Returns 6-123 4-119

Interceptions Ret. 1-32 1-0

Comp-Att-Int 23-44-1 26-48-1

Sacked-Yards Lost 2-9 2-20

Punts 9-45.1 9-43.7

Fumbles-Lost 2-1 1-1

Penalties-Yards 6-46 5-44

Time of Possession 36:01 38:55

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INDIVIDUAL STATISTICS

RUSHING—Cincinnati, Benson 18-74, Scott 6-41, C.Palmer 3-20, Caldwell 1-11, J.Johnson 1-4, Leonard 1-4. Cleveland, Harrison 29-121, Cribbs 1-15, Jennings 1-8, Anderson 2-2.

PASSING—Cincinnati, C.Palmer 23-44-1-230. Cleveland, Anderson 26-48-1-269.

RECEIVING—Cincinnati, Leonard 6-28, Coats 4-36, Foschi 3-44, Ochocinco 3-24, Henry 2-36, Caldwell 2-26, Coles 2-24, Benson 1-12. Cleveland, Massaquoi 8-148, Heiden 5-33, Harrison 5-31, Furrey 4-37, Royal 2-13, Cribbs 1-5, Jennings 1-2.

MISSED FIELD GOALS—Cincinnati, Graham 23 (BK).