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The Steelers took the lead on their first possession through a Chris Boswell field goal, but they lost quarterback Landry Jones to an ankle injury, forcing Roethlisberger off the bench to play through the pain barrier of a foot problem.
The sides exchanged field goals at the end of first quarter to leave the match open, but the home side made the first telling blow of the contest when they capitalised on a costly error from Armonty Bryant as Roethlisberger found Antonio Brown in the endzone.
Cleveland made a solid stand on their goalline to prevent a second score from Pittsburgh, but it only stemmed the tide for two minutes before Roethlisberger lofted the ball deep for Martavis Bryant to complete a 32-yard touchdown.
Boswell extended the home side's advantage to 21 points at the start of the third, but Cleveland responded with a drive from Johnny Manziel, who almost found the endzone with a strong solo run before he was tackled by Cam Thomas.
Isaiah Crowell looked to have scored a touchdown on the next play, but a penalty nullified the score. Another error from the Browns moved them further back from the goalline, while their drive was ended when Manziel was picked off by Mike Mitchell.
However, Manziel responded on the next drive when he lofted a fade to the back of the endzone for Gary Barnidge to make the catch for a seven-yard touchdown, although Travis Coons missed the extra-point kick.
The Steelers ended any hope of a comeback for Mike Pettine's men when Brown recorded his second touchdown of the game by collecting a short pass from Roethlisberger before speeding past two defenders to reach the endzone.
Pittsburgh move to 6-4 in their season with the victory, while the Browns drop to 2-8.