Peete threw for all three of his touchdowns and 237 yards in the second half, during which the Panthers (5-8) erupted for 36 points.
"It was a great game, definitely a game where we had it working on all cylinders," said Peete, who completed 21 of 29 passes and fell four yards shy of his career-high for yards. "They came out trying to stop the run. The offensive line gave me time and guys got open."
Smith, who was suspended by the team for one game for punching a teammate during a film session last month, set a club record with his 87-yard punt return for a touchdown in the third quarter after scoring on a 61-yard punt return in the second period.
He also caught a 31-yard touchdown 1:57 into the second half and finished with five receptions for 144 yards.
But Smith's second year in the NFL was marred by an ugly incident in which he beat up teammate Anthony Bright after the two engaged in an argument during a team film session. Bright was hospitalized for two days with a broken nose and fractured bone near the eye socket and officially filed charges.
Smith was suspended one game by the team, although some players believed stiffer discipline was warranted. He returned to the team last week after serving the suspension and was not warmly welcomed by some teammates. However, after his three touchdowns on Sunday, Smith received hugs from most of the players.
"I don't have to show the team anything, they showed me that they trust me by letting me play," Smith said. "I'm just trying to be a pro. I've got to remember how fortunate I am to be in the NFL."
Peete also connected with Muhsin Muhammad and tight end Wesley Walls on scoring passes of three and two yards in the second half. Muhammad finished with eight catches for 106 yards.
"They loaded up for the run, Rodney threw the ball and the guys made plays," said Panthers Coach John Fox.
Carolina's previous high was 45 points, set on Oct. 13, 1996 against St. Louis and matched on Jan. 2, 2000 against New Orleans.
Along with the special teams breakdowns, the Bengals (1-12) allowed a fumble recovery for a touchdown, committed two other fumbles and yielded a safety. They were last 1-12 in 1993.
Cincinnati's Jon Kitna was 25 of 37 for 295 yards and two touchdowns, both to Peter Warrick, and ran for another score.
The Panthers compiled a season-high 401 total yards and improved to 3-0 against AFC North teams.
The defense and special teams accounted for Carolina's 16 points in the first half before the offense exploded for 36 points in the second half.
"Coach really challened us at halftime and we needed to be challenged," Walls said. "We came out in the second half rolling and it just snowballed from there."
The Panthers actually could have scored more, but Fox instructed Peete to take a knee at the Cincinnati one the final minute.
Defensive end Al Wallace, who was replacing the suspended Julius Peppers, recovered a fumble in the end zone for a touchdown and end Mike Rucker tackled Corey Dillon in the end zone for a safety in the first quarter.
Carolina increased its lead to 16-7 on Smith's first punt return touchdown 1:13 into the second quarter. After juking past the initial wave of defenders, Smith raced down the right sideline.
But Warrick, who earlier caught a 37-yard touchdown in the first quarter, had a three-yard scoring reception in the second quarter and Neil Rackers added a 24-yard field goal to give the Bengals a 17-16 lead.
Cincinnati had 16 first downs to six for Carolina and outgained the Panthers, 249-115, in the first half.
"We dominated the game in the first half and fell apart in the second half," Kitna said.
"We had the game going into halftime and we just expected to be able to control the game in the second half," said Bengals receiver Chad Johnson, who had six catches for 114 yards.
Peete connected with Smith on a 31-yard touchdown 1:57 into the second half, but the Bengals reclaimed the lead when linebacker Takeo Spikes returned a fumble 45 yards for a touchdown less than two minutes later.
The Panthers took the lead for good when Peete capped a nine-play, 76-yard drive with a two-yard touchdown throw to Muhammad 5:37 left in the third quarter. After Cincinnati went three-and-out, Smith scored on his 87-yard punt return to increase the lead to 37-24 with 4:24 remaining. Winslow Oliver held the club record with an 84-yard punt return in 1996.
Jennifer Lawrence: 'It should be illegal to call somebody fat on TV'
Topless Snapchat photo of mother and 14-year-old daughter leads to charges