The Steelers got on the board on Suisham's 27-yard field goal with 13:36 left in the second quarter, but the Bears answered when Wright returned an interception 38 yards for a touchdown a little more than 3 1/2 minutes later to put Chicago on top 24-3.
Roethlisberger threw a 33-yard touchdown pass to Brown with 6:27 to go, drawing the Steelers within 24-10 at halftime.
After the teams traded field goals in the third quarter -- Gould connected from 32 yards, then Suisham hit from 36 -- the Steelers got within a touchdown at 27-20 when Brown made a spectacular one-handed grab of a Roethlisberger pass in the back of the end zone for a 21-yard score with 1:50 left in the third.
"It was a very difficult game in a very tough environment to win, and we feel very grateful that we could come out on top here," Trestman said.
NOTES: Pittsburgh TE Heath Miller started after sitting out the first two games while recovering from reconstructive knee surgery performed last December. He caught three passes for 35 yards. ... Bears FS Chris Conte had eight tackles, an interception and two passes defensed. Williams had two sacks. ... Steelers LB Lawrence Timmons was in on nine tackles and broke up two passes. ... WR Derek Moye, who scored one of the Steelers' two touchdowns the first two weeks of the season, was inactive along with RB Le'Veon Bell (foot), CB Cortez Allen (ankle), QB Landry Jones, CB Isaiah Green, OL Cody Wallace and DT Hebron Fangupo. ... Chicago's inactivates were WR Marquess Wilson, CB C.J. Wilson, RB Michael Ford, G James Brown, OT Jonathan Scott, DE David Bass and DT Zach Minter. ... The Bears visit the Detroit Lions on Sunday. Pittsburgh travels overseas to play the Minnesota Vikings in London.