McCaffrey produced his first NFL career rushing total of more than 100 yards on 28 carries, and quarterback Cam Newton added two rushing touchdowns while passing for two more, including a short connection with running back C.J. Anderson.
Newton, who was 15-of-24 for 150 passing yards, won his seventh straight home start.
"We can't let off the pedal. We have to get guys back, keep guys healthy," Newton said of the Panthers' upcoming bye week.
Carolina was also successful thanks to an opportunistic defense with four takeaways, including two interceptions by rookie cornerback Donte Jackson. Reserve defensive lineman Efe Obada, a former practice player with the Atlanta Falcons and New Orleans Saints playing in the first NFL game of his career, had a sack and an interception for the Panthers.
Obada's interception of Cincinnati's Andy Dalton late in the third quarter set up a 5-yard scoring run by Newton, putting the Panthers up 28-14.
On the ensuing drive, Dalton found wide receiver Tyler Boyd in the end zone to put Cincinnati within a touchdown heading into the fourth quarter. Boyd had six receptions for 132 yards.
Dalton tried to target Panthers safety Colin Jones, who is a role player and special teams standout. He replaced Da'Norris Searcy in the starting lineup after Searcy was placed on IR last week.
After a sack on Dalton by Obada with under four minutes remaining, Jackson would nab his third career interception. A 40-yard Graham Gano field goal secured the win for Carolina heading into its bye week.
"The pass rush really came up big," Carolina head coach Ron Rivera said of the Panthers' two sacks and constant pressure.
Dalton threw four interceptions, and the Bengals were also impacted by the loss of receiver A.J. Green, who left the game early in the third quarter and did not return because of a groin injury.
Green tried to make a leaping catch over the middle and it looked like Jackson hit him early. The ball went one way and Green seemed to land awkwardly the other way.
"I came down on my hip, I guess my two bones just hit against [each other]. I should be fine," Green said. "I didn't feel anything pop or anything like that, so I should be fine."
Asked if he will play next week at the Atlanta Falcons, Green said, "Oh yeah. I'll be fine."
The Bengals' running game also struggled with Gio Bernard, filling in for the injured Joe Mixon, leading the team with 61 yards on 12 carries.
Cincinnati scored first after back-to-back defensive holding penalties. Bernard capped an 11-play, 75-yard opening drive with a 1-yard touchdown plunge.
On the Panthers' second drive, a pair of rushes from McCaffrey ignited the offense. McCaffrey recorded a 13-yard run for a first down and then had a 45-yarder -- the longest of his career -- to put Carolina in scoring position. Newton scored on a 2-yard run to end the nine-play, 75-yard drive.
"[McCaffrey's] ability to run the ball inside, he doesn't get enough credit for it," Rivera said.
The Bengals' attempt to answer was halted near the end of the first quarter after Jackson picked off Dalton. The interception was Dalton's first of the season.
The offense capitalized by driving 67 yards and scoring on a 4-yard Newton pass to wide receiver Devin Funchess to put Carolina up 14-7 early in the second quarter. Midway through the second quarter, Cincinnati converted another 75-yard drive into a touchdown after Dalton found tight end C.J. Uzomah to tie the game at 14.
Dalton finished the game 29-of-45 for 352 yards and two touchdowns to go with his four interceptions.
A 24-yard Newton screen pass to Anderson gave the Panthers a 21-14 halftime lead, capping off the fourth 75-yard scoring drive of the first half.
NOTES: With three tackles today, LB Luke Kuechly moved into third all-time in Panthers' franchise history with 839 career tackles. Thomas Davis is the team's all-time leader with 1,174 tackles, and Mike Minter is second with 953. ... RB Christian McCaffery's career-high 184 yards rushing against Cincinnati was his first game with more than 100 yards. His previous high was 66 yards.