The signal caller threw three first-half interceptions but also scored a rushing touchdown, before a much-improved second half completed the job.
Dalton threw his first pick within the first 10 seconds of the match, shooting straight into the arms of Johnthan Banks. Although Banks ran the ball back deep into Bengals territory, they had to settle for a Patrick Murray field goal to open the scoring.
Following more struggles on Bengals offense, the home side scored the first touchdown of the day, with running back Doug Martin carrying in a seven-yard attempt.
On their next red zone trip, the quarterback decided to run it in himself, faking a handoff to Giovani Bernard and rushing for six points.
Dalton was picked off once more before the break, but improved after half time, quickly leading the Bengals downfield, culminating in a 13-yard touchdown pass to Green.
Murray kept the Buccaneers in the contest, scoring his second field goal of the day right at the beginning of the final quarter.
Both Dalton and Tampa quarterback Josh McCown did their best to keep their offenses moving during the last 15 minutes, resulting in no further points as the game headed into the two-minute warning.
McCown's two-minute drill provided thrills and spills via catches and penalties, but in the end the Bengals held on and managed to avoid conceding a field goal shot.