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Justin Tucker added another three points for his side in the first quarter before Flacco threw his second touchdown pass of the night, finding Torrey Smith with a seven-yard throw in the second quarter to give his side a 17-0 lead at the halfway stage.
The Bengals finally registered on the scoreboard at the start of the second half when Mike Nugent hit a 32-yard field goal, but that was to be the final score of the third quarter as both defenses held firm.
Cincinnati then gave themselves a glimmer of hope by reducing the deficit to seven points with 8:30 left in the fourth quarter, Giovani Bernard catching Andy Dalton's short pass before showing great pace to beat a number of tackles on his way to the end zone.
The Bengals then pulled off an incredible late comeback with just two seconds left. Dalton launched a 51-yard Hail Mary pass into the end zone that deflected off two pairs of hands before being caught by AJ Green to force overtime.
It was the Ravens who were to have the last laugh, however, as Tucker kicked a 46-yard field goal in overtime to clinch an important victory for the reigning Super Bowl champions.