CINCINNATI — Sam Cooke’s song ‘‘A Change is Gonna Come’’ played on a continuous loop in the Cincinnati Bengals’ locker room, providing the musical score for a groundbreaking win.

In five frenetic minutes, the Bengals earned some legitimacy and won back their town.

Carson Palmer’s 4-yard touchdown pass to Andre Caldwell with 14 seconds left provided a 23-20 win Sunday that ended the Pittsburgh Steelers’ nearly decade-long domination in Cincinnati, one that appeared set to go on indefinitely until the final drive.

‘‘Priceless,’’ offensive lineman Bobbie Williams said. ‘‘The past is the past. This is a new team and a new day.’’

For once, it was their day.

Pittsburgh (1-2) had won its last eight games on Cincinnati’s home field. The last time the Bengals beat them at Paul Brown Stadium was 2001, when Chad Ochocinco was a rookie who rarely started and still went by the name of Johnson.

Ochocinco doesn’t remember much from that long-ago game. The Bengals (2-1) won’t soon forget this one.

The defending Super Bowl champs dominated most of the game but wasted chances to put the Bengals away. Jeff Reed missed another field goal, and Limas Sweed dropped a pass in the end zone, keeping it close to the end.

‘‘If we score touchdowns in the first half, it’s not even a game,’’ Steelers receiver Hines Ward said. ‘‘It’s 24-0 or 24-3. It’s not very good. You’ve got to put up seven points instead of 3s. That’s how you finish a team off.’’

Instead, the Bengals finished them off.

Palmer led the Bengals on a 16-play, 71-yard drive against one of the league’s best defenses, repeatedly converting there-or-else throws. His 11-yarder to running back Brian Leonard on fourth-and-10 moved the ball to the 4. After a spike to stop the clock, Palmer found Caldwell open in the middle of the end zone.

‘‘We’ve got a quarterback who’s comfortable at those points in the game,’’ coach Marvin Lewis said. ‘‘He’s got a calm about him.’’

It was reminiscent of Palmer’s long touchdown drive at the end of the season opener against Denver, which the Broncos then salvaged with a tipped, 87-yard touchdown catch. This time, there would be no weirdness.

Ben Roethlisberger’s final, frantic heave was knocked down, giving the Bengals a game they viewed as a chance to prove that they can contend in the AFC North.

‘‘It’s huge,’’ defensive lineman Tank Johnson said. ‘‘This team is a very good football team. If we eliminate the immature mistakes, the sky is the limit.’’

Beating the Steelers at home was no small thing. Thousands of Steelers fans were sprinkled throughout the crowd of 64,538, waving their yellow towels almost nonstop as Pittsburgh dominated but repeatedly failed to take advantage of scoring chances.

And, in the end, the defense failed to make a play to finish off the Bengals, reminiscent of the way Pittsburgh missed two second-half field goals in Chicago, then let the Bears pull out a 17-14 win on a field goal with 15 seconds left.

‘‘We strive to be a great defense and make those plays,’’ defensive end Brett Keisel said. ‘‘If we don’t start making them, it’s going to be a long year.’’

When Roethlisberger and Santonio Holmes had a miscommunication on the third play of the second half — the quarterback made a quick throw, the receiver kept going — cornerback Johnathan Joseph intercepted and ran 30 yards for a touchdown that made it a game.

Roethlisberger was 22 of 31 for 276 yards, including a 39-yard touchdown pass to Willie Parker and a 1-yard scoring sneak. He was sacked near midfield on a third-down play as Pittsburgh tried to protect a 20-15 lead, giving the Bengals one last chance with 5:14 to play.

All they needed.

‘‘Indescribable,’’ said Palmer, who was 20 of 37 for 183 yards. ‘‘The fans wanted it as much as we did, and it felt great to see those hands go up signaling a touchdown and hear them roar.’’

The Steelers hadn’t started 1-2 since 2006, the last time they were coming off a Super Bowl win. They opened 1-3 that season and finished 8-8, missing out on the playoffs. With two straight last-minute losses, the Steelers are again finding out how tough it is to be a defending champ.

‘‘We feel like we beat ourselves,’’ Roethlisberger said.

NOTES: It was Roethlisberger’s first loss as a Steelers QB in his native state of Ohio. He had been 11-0 in Cleveland and Cincinnati. … Ward became the first Steeler to have 10,000 yards in catches during his career. … Steelers rookie WR Mike Wallace had seven catches for a career-high 102 yards. … Bengals rookie LB Rey Maualuga was carted off the field with a left knee injury in the second half, but returned to the field a series later.

Pittsburgh 10 3 7 0—20

Cincinnati 0 3 6 14—23

First Quarter

Pit—FG Reed 19, 6:55.

Pit—Parker 27 pass from Roethlisberger (Reed kick), 1:02.

Second Quarter

Pit—FG Reed 24, 12:44.

Cin—FG Graham 34, :00.

Third Quarter

Cin—Joseph 30 interception return (run failed), 13:35.

Pit—Roethlisberger 1 run (Reed kick), 3:00.

Fourth Quarter

Cin—Benson 23 run (pass failed), 9:14.

Cin—Caldwell 4 pass from C.Palmer (Leonard pass from C.Palmer), :14.

A—64,538.

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Pit Cin

First downs 17 19

Total Net Yards 373 273

Rushes-yards 28-102 19-100

Passing 271 173

Punt Returns 0-0 1-17

Kickoff Returns 4-110 5-104

Interceptions Ret. 0-0 1-30

Comp-Att-Int 22-31-1 20-37-0

Sacked-Yards Lost 1-5 2-10

Punts 2-42.5 5-40.8

Fumbles-Lost 0-0 0-0

Penalties-Yards 5-51 4-30

Time of Possession 34:42 25:18

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INDIVIDUAL STATISTICS

RUSHING—Pittsburgh, Parker 25-93, Moore 1-6, Roethlisberger 2-3. Cincinnati, Benson 16-76, Crocker 1-21, J.Johnson 1-2, C.Palmer 1-1.

PASSING—Pittsburgh, Roethlisberger 22-31-1-276. Cincinnati, C.Palmer 20-37-0-183.

RECEIVING—Pittsburgh, Wallace 7-102, Miller 5-20, Ward 4-82, Parker 2-36, Holmes 1-18, Spaeth 1-7, Moore 1-6, Sweed 1-5. Cincinnati, Caldwell 6-52, Ochocinco 5-54, Coles 5-34, Henry 1-19, Leonard 1-11, Coats 1-8, Benson 1-5.

MISSED FIELD GOALS—Pittsburgh, Reed 52 (WL). Cincinnati, Graham 52 (WL).