The last-minute Bengals needed a 31-yard field goal from Shayne Graham late in overtime to beat the winless Cleveland Browns 23-20 on Sunday.
Not wanting to settle for a tie, Bengals coach Marvin Lewis gambled and decided to go for it on fourth-and-11 from the Cleveland 41 with 1:04 remaining.
Palmer dropped back to pass and then tucked the ball away and scampered up the middle for 15 yards and the first down. Cincinnati ran two plays to get Graham in position, and the kicker, who had an extra point and field goal blocked earlier in the game, sent it sailing through the uprights.
"It'd be nice to go up by a couple scores and drink some Gatorade as we take a knee at the end," Palmer said.
Defensive end Robert Geathers returned a fumble 75 yards for a score for Cincinnati (3-1), which is tied with Baltimore atop the AFC North. The Bengals visit the Ravens next Sunday.
"Nobody's happy," said Browns 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."
Anderson, making his first start since coach Eric 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.
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 had only one other catch in the game.
Saints 24, Jets 10
At New Orleans, Darren Sharper returned one of his two interceptions of rookie Mark Sanchez 99 yards for a score, Will Smith forced a fumble in the end zone to produce a second defensive touchdown, and New Orleans handed the Jets their first loss.
New York (3-1) lost despite stopping the Saints twice on fourth-and-short and holding Drew Brees to 190 yards passing and no touchdowns. New Orleans' normally high-powered offense, which entered the game ranked first in the NFL, did not score a touchdown until Pierre Thomas barreled in from a yard out with 6:07 left.
Sanchez completed 14 of 27 passes for 138 yards and doomed the Jets with four turnovers.
Broncos 17, Cowboys 10
At Denver, Champ Bailey knocked away a potential tying touchdown pass from Tony Romo to Sam Hurd with 1 second left. On fourth-and-goal from the 2, Romo found Hurd cutting over the middle, but Bailey reached around and swatted the pass away at the last second, giving the Broncos their first 4-0 start since 2003.
The Broncos took the lead on Brandon Marshall's 51-yard touchdown catch with 1:46 remaining.
The Cowboys (2-2) were ranked first in the league in rushing, but managed only 74 yards on the ground.
Steelers 38, Chargers 28
At Pittsburgh, Ben Roethlisberger threw touchdown passes on the first two drives, Rashard Mendenhall surpassed his previous career total with 165 yards rushing and two scores and the Steelers held on after squandering a 28-point lead.
The Chargers (2-2), outgained nearly 4 to 1 until late in the third quarter, rallied as Philip Rivers threw touchdown passes of 30 yards to Antonio Gates and 13 yards to Chris Chambers and Jacob Hester scored on a 41-yard fumble return, all in the fourth quarter.
Running back Mewelde Moore caught a touchdown pass and threw for another to Heath Miller on a goal-line play as the Steelers (2-2), beaten in the closing seconds by Chicago and Cincinnati the previous two weeks, built such a big lead that they withstood another bad fourth quarter.
49ers 35, Rams 0
At San Francisco, tight end Vernon Davis caught a 13-yard pass for his third touchdown in two weeks, Patrick Wills returned an interception 23 yards for a score and the 49ers overcame the absence of star running back Frank Gore.
The 49ers (3-1) scored in every way to take command of the NFC West, recording their first shutout in 119 games since Jan. 6, 2002, 38-0 at New Orleans.
The Rams (0-4) lost their 14th straight, the longest current skid in the NFL.
Dolphins 38, Bills 10
At Miami, quarterback Chad Henne making his first NFL start and the Dolphins controlled the ball for 37 minutes to earn their first victory.
The Dolphins came into the game 0-3 despite a strong running attack and an 11-minute edge per game in time of possession. Against Buffalo (1-3), Miami ran for 250 yards and mounted scoring drives of 65, 66 and 65 yards.
Henne, a second-year pro, shook off six sacks and managed the game well in his first start in place of injured Chad Pennington. Henne had no turnovers, and he threw his first NFL touchdown pass, a 5-yarder to rookie Brian Hartline.
Patriots 27, Ravens 21
At Foxborough, Mass., Tom Brady and Randy Moss hooked up for their first touchdown pass of the season and Baltimore failed on fourth-down plays on its last two series.
Moss' touchdown made it 24-14 late in the third quarter, but Joe Flacco's 13-yard pass to Willis McGahee cut that to 24-21. Stephen Gostkowski's 33-yard field goal gave the Patriots (3-1) a six-point lead midway through the fourth quarter.
On the next possession, with a fourth-and-1 at the Ravens 45-yard line, McGahee was stopped for no gain. The Ravens (3-1) got the ball back after a punt and moved to a fourth-and-4 at the 14. Flacco then threw to Mark Clayton, who dropped the ball with 28 seconds remaining.
Jaguars 37, Titans 17
At Jacksonville, Fla., David Garrard threw for 323 yards and three touchdowns, two to Mike Sims-Walker.
Garrard shredded Tennessee's injury depleted secondary, often picking on rookie cornerback Jason McCourty, and Jacksonville's defense dominated the Titans (0-4). Tennessee went 13-3 last season, the league's best record, and didn't lose until Game 11.
Colts 34, Seahawks 17
At Indianapolis, Peyton Manning led the Colts on four touchdown drives, tied milestones established by Fran Tarkenton and Dan Marino and extended his team's regular-season victory streak to 13.
Manning finished 31 of 41 for 353 yards, marking the first time in 12 NFL seasons he has topped 300 yards in four consecutive games.
The first TD pass went to Reggie Wayne, making Manning and Dan Marino the only quarterbacks in league history to throw 55 TD passes to two different receivers. The second went to rookie Austin Collie after a brilliant audible with 3 seconds left in the half. It not only gave the Colts (4-0) a 21-3 halftime lead but also gave Manning a share of third place on the NFL's career touchdowns passing list with Tarkenton. Both have 342.
Only Marino (420) and Brett Favre (469) have thrown more.
Seattle (1-3) played without quarterback Matt Hasselbeck and left tackle Walter Jones, who are both hurt, and lost its third straight.
Giants 27, Chiefs 16
At Kansas City, Mo., Eli Manning, before leaving in the fourth quarter with a bruised right heel, threw for 292 yards and three touchdowns as the Giants (4-0) remained unbeaten.
Kansas City (0-4) has lost 27 of its last 29 games.
Matt Cassel threw two short touchdown passes in the final minutes for Kansas City.
Steve Smith, who has caught at least one scoring pass in three straight games for the Giants, totaled 134 yards on 11 catches, including scoring receptions of 3 and 25 yards.
Redskins 16, Buccaneers 13
At Landover, Md., Jason Campbell made up for a pair of first-half interceptions with two second-half touchdowns, and the Redskins (2-2) scored on three straight possessions for the first time this season.
Trailing 10-0 after a first half, the Redskins sarted their rally when DeAngelo Hall intercepted a pass from second-year quarterback Josh Johnson, making his first NFL start. Washington converted the turnover into a field goal, then Campbell hit Chris Cooley for a 17-yard touchdown and Santana Moss for a 59-yard score on the next two series. Aqib Talib's third interception of the game led to a field goal to cut the lead to 16-13 with 4:25 to play. Tampa Bay got the ball back after a punt, but Clifton Smith fumbled deep in his territory to end the Buccaneers' final chance.
Texans 29, Raiders 6
At Houston, Steve Slaton scored two touchdowns, Jacoby Jones returned a kickoff for a score and the Texans (2-2), with the NFL's worst defense, held the Raiders to 45 yards rushing. The Texans were allowing 205 yards rushing entering the game.
Houston also forced three turnovers and got its first safety in almost seven years.
The Raiders (1-3) continued to struggle, with JaMarcus Russell completing 12 of 33 passes for 128 yards and Darren McFadden finishing with six carries for minus-3 yards rushing.
Bears 48, Lions 24
At Chicago, Jay Cutler threw two touchdown passes and ran for another score, and the Bears pulled away in the second half a week after Detroit snapped its 19-game losing streak.
Matt Forte ran for 121 yards and rookie Johnny Knox returned a kickoff 102 yards.
Lions rookie quarterback Matthew Stafford left during the fourth quarter because of a leg injury.