Fernando Pisani, Patrick Sharp and Patrick Kane also scored for Chicago (2-4-0).
Crawford, poised to back up veteran goalie Marty Turco this season, lost a shutout bid with 9:20 left in the third period when Pittsburgh's Alex Goligoski converted a rebound for a power-play goal. The 25-year-old made a handful of tough saves against a Pittsburgh lineup that didn't include star forwards Sidney Crosby and Evgeni Malkin.
Craig Adams added a late goal for the Penguins (4-1-0). Marc-Andre Fleury, Pittsburgh's No. 1 goalie, played the first two periods and allowed two goals on 16 shots. Brent Johnson played the third and gave up three goals on 10 shots.
Chicago defenseman Brian Campbell left the game early in the second period with an undisclosed injury and did not return.
Blackhawks coach Joel Quenneville didn't elaborate on Campbell's condition after the game.
"We'll see," Quenneville said. "He's going to be re-evaluated by the doctors tomorrow. He was hit along the boards and it didn't look like it was malicious."
Asked if Campbell would be available for Chicago's regular-season opener Thursday in Colorado, Quenneville again said, "We'll see."
Pittsburgh forward Arron Asham suffered an upper-body injury in the game and will be re-evaluated by doctors on Saturday, a team official said.
The Blackhawks lineup included all of the team's big-name stars from last year's Stanley Cup championship team,and most of the regulars who figure to be with the club when it opens the season Thursday at Colorado.
Fleury made two point-blank saves -- on Viktor Stalberg and Jonathan Toews -- in the scoreless first.
Pisani opened the scoring at 4:20 of the second. He completed a rush by firing a one-time shot over Fleury's glove after taking a feed from Dave Bolland.
Sharp's power-play goal made it 2-0 with 6:13 left in the period. He picked off a botched Pittsburgh clearing attempt near the right point and beat Fleury through a screen.
Crawford made his toughest saves with about 7:30 left in the second, blocking Matt Cooke's shot from the circle and Eric Godard's rebound attempt from the crease.
Hossa extended Chicago's lead to 3-0 just 19 seconds into the third by outracing Pittsburgh defenseman Simon Despres to a loose puck on the right boards and then driving to the net.
Kane lofted in a power-play goal at 5:56 of the third to make it 4-0.
Goligoski made it 4-1 scoring by firing in a rebound after Crawford blocked Michael Rupp's shot.
Adams closed in to 4-2 with 1:18 left, but Hossa replied with his second goal 18 seconds later.