The running-back put the hosts ahead before tight end C.J. Uzomah caught a one-yard touchdown reception at the end of the first quarter.
Cincinnati took a 17-point advantage into the final quarter, Kenneth Dixon scored a touchdown to make it a nervous finish.
However, Burkhead added his second score of the game to ensure the Bengals would close out the season with a win against their AFC North rivals.
Veteran receiver Steve Smith Sr played his final NFL game and called it a day after the game, and the visibly emotional Raven has had one illustrious career.
Bengals race into early lead
After the season-ending defeat to the Pittsburgh Steelers in Week 16, Baltimore had only pride to play for when they travelled to face the Bengals.
They started with a three-and-out before Cincinnati scored on their first drive of the game when they took full advantage of a short field.
Andy Dalton threw to Burkhead, who managed to keep his balance going backwards and the running-back managed to break into the end zone for a five-yard touchdown.
Justin Tucker kicked a 30-yard field goal to put the visitors on the board before Dalton threw his second touchdown pass of the game, this time to Uzomah for a one-yard reception.
Randy Bullock followed up with two field goals of his own before half-time to take the home side into the break with a dominant lead against their divisional rivals.
Flacco sets franchise record
During a scoreless third quarter, Ravens quarterback Joe Flacco broke the single-season record for passing yards, surpassing Vinny Testaverde’s record of 4,177-yards back in 1996.
With nothing to left, Baltimore faced a fourth-and-short situation with minutes left in the third, but the Bengals defense stepped up and forced a turnover on downs.
John Harbaugh’s side made it a two-score game with over nine minutes left on the clock moments after they had a touchdown overturned.
Breshad Perriman’s catch and run for a 40-yard score was called back as his elbow was down short of the goalline, but two plays later, they scored their first touchdown of the game.
Dixon rushes for touchdown in fourth quarter
Dixon rushed up the middle and bounced off a tackle before breaking into the end zone for his second touchdown of the season.
The hope for the Ravens was short-lived as the visitors failed on a fourth down conversion on their own 25-yard line and the Bengals made the most of a short field once more.
Burkhead rushed up the middle for a five-yard touchdown to seal the victory with minutes remaining, and Ryan Mallett came in at quarterback for the final few plays.
The back-up threw an interception to KeiVarae Russell and that confirmed victory for Cincinatti, who ended the season 6-9-1, while the Ravens finished second in the division at 8-8.