Roethlisberger completed 17-of-24 passes, including one to Brown for a score. Brown, who finished with 108 yards on seven receptions, also caught a TD pass from Byron Leftwich, who completed 5-of-8 passes for 105 yards.
Ryan Fitzpatrick passed for 89 yards, completing 7-of-18 attempts for Buffalo.
Fred Jackson scored the Bills' only touchdown with a 1-yard run in the first quarter.
Notable deaths of 2014 [PHOTOS]
LeBron James reveals his new Nike shoes