Safety Wright picked off a Ben Roethlisberger pass in the second quarter and ran it back 38 yards for a score, handing the Bears a 24-3 lead.
Then, after the Steelers narrowed the deficit to four points in the fourth quarter, Jay Cutler connected with Earl Bennett on a 17-yard TD pass and defensive end Peppers iced the contest with a 42-yard return for a score off a Roethlisberger fumble.
The Bears forced four Pittsburgh turnovers in all in moving to 3-0 to begin the season for the just the third time in 20 years.
Cutler finished 20-for-30 passing for 159 yards and a TD while Matt Forte paced the ground game with 87 yards and a score on 16 carries.
Roethlisberger went 26-of-41 through the air for 406 yards with two TDs, two interceptions and two lost fumbles as the Steelers fell to 0-3 for the first time since 2000.
Antonio Brown made nine catches for 196 yards and two touchdowns in the loss.