(Reuters) - Josh Brown booted a 43-yard field goal with four seconds left to play to earn the Cincinnati Bengals a 13-10 win over the Pittsburgh Steelers and a ticket to the National Football League playoffs on Sunday.

The victory was the Bengals' (9-6) first over their bitter AFC North rivals in six meetings and left a capacity crowd at Heinz Field stunned with the loss that eliminated the Steelers (7-8) from post-season contention.

As is typical when the Steelers and Bengals clash, the meeting was a bruising defensive battle, the Cincinnati defense accounting for the Bengals' only touchdown when Leon Hall intercepted Ben Roethlisberger in the opening quarter and returned it 17 yards for the score.

Roethlisberger connected with Antonio Brown on a 60-yard touchdown in the third quarter to get Pittsburgh back into the contest but made a fatal mistake with 14 seconds to play, throwing his second interception that was returned to the Steelers 46 to set up Brown's game-winning kick.

(Reporting by Steve Keating in Toronto; editing by Gene Cherry)