Tom Brady's team led early in the game, with the star quarterback throwing for his own two touchdowns in the second quarter.
But momentum was all with the Bengals from the third, with Burrow finding Tee Higgins, Tyler Boyd, Ja'Marr Chase and Mitchel Wilcox in the end zone.
Meanwhile, the Kansas City Chiefs beat the Houston Texans in overtime to claim the AFC West title.
Running back Jerick McKinnon got the Chiefs over the line with a 26-yard touchdown run.
It is the seventh-straight division win for Kansas City.
The Las Vegas Raiders were victorious over the New England Patriots 30-24.
While the Raiders led for most of the game, the Patriots looked set for a comeback in the final quarter that would push the game into overtime.
That was before wide receiver Jakobi Meyers accidentally handed opposing defensive end Chandler Jones a 48-yard fumble return touchdown.
The Jacksonville Jaguars eclipsed the Dallas Cowboys 40-34 on the back of a crucial Raysharn Jenkins interception.
He picked off Dak Prescott's pass in overtime, returning it 52 yards for a touchdown.
It was Jenkins' first pick six in his career.
In other games, the Buffalo Bills narrowly defeated the Miami Dolphins 32-29, the Chicago Bears lost to the Philadelphia Eagles 25-20, and the New Orleans Saints beat the Atlanta Falcons 21-18.
The Detroit Lions triumphed over the New York Jets 20-17, the Carolina Panthers lost to the Pittsburgh Steelers 16-24, and the Denver Broncos defeated the Arizona Cardinals 24-15.
Elsewhere, the Los Angeles Chargers just escaped the Tennessee Titans 17-14, while the New York Giants beat the Washington Commanders 20-12.