The Bears defense forced five Pittsburgh turnovers and scored two touchdowns in a wild game that vaulted them to 3-0.
Chicago raced out to a 17-0 lead in the first quarter and led 24-3 in the second before Steelers' quarterback Ben Roethlisberger connected on a 33-yard touchdown to Antonio Brown to spark a comeback.
Roethlisberger finished with 406 yards passing while Brown had 196 yards receiving and two scores.
Brown also had a one-handed, 21-yard touchdown grab in the third, and after Shaun Suisham kicked his third field goal of the game Pittsburgh had pulled to within 27-23 early in the fourth.
But the Bears sealed it when Earl Bennett made an acrobatic 17-yard catch along the sideline to put the visitors ahead 34-23, and Julius Peppers returned a fumble 42 yards for the final score of the game.
Chicago's Major Wright helped lead the opportunistic defense with a 38-yard interception return for a touchdown, along with a forced fumble.