The visitors to the Paul Brown Stadium scored 25 unanswered points in the final quarter to take the game beyond the Bengals, having exchanged the lead up until that point.
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Dalton took matters into his own hands with just under three minutes remaining in the third quarter, bursting through the middle and racing into the endzone for a 20-yard touchdown.
Shaun Suisham reduced the deficit to four shortly before the interval with a 22-yard field goal, and Pittsburgh regained the lead after the break when Bell collected a short pass from Roethlisberger and found the corner of the endzone.
AJ Green had been enjoying a productive day for the hosts, and he put his side back in front in style as time ran out in the third quarter, collecting a long Dalton pass before cutting inside and strolling in for an 81-yard score.
Suisham kicked a 44-yard field goal early in the fourth quarter to make it a one-point game, and Bell was once again the man to restore his side's lead with a bruising 13-yard run that ended with him reaching over the line for a score.
The Steelers gave themselves some breathing space shortly afterwards as Roethlisberger's long pass was hoisted in by Martavis Bryant, who took it all the way down the right touchline for a 94-yard score.
They put the game beyond doubt with another touchdown in a successful final quarter as Bell ran it in from 22 yards to make it three on the night for him.
The victory sees Pittsburgh move level with the Bengals on eight wins as the playoff picture in the AFC North heats up.