Rick Nash and Jakub Voracek each had a goal and an assist while Samuel Pahlsson and Antoine Vermettealso scored for the Blue Jackets, who have won three straight.
"We'll take a win in this building against a real good club," said Columbus head coach Scott Arneil. "We came out strong and never let up. It was a real solid road game for us."
Tyler Kennedy scored the lone goal while Marc-Andre Fleury made 21 stops for the Penguins, who have dropped their past two games after winning five straight.
"We expected them to come out strong tonight and they did," Fleury said.
The Blue Jackets got on the board 6:07 in when Derick Brassard fed a hard pass from the top of the left circle to the low right circle where Nash snapped a one-timer into the net.
Matt Cooke was assessed a major for boarding when he slammed Fedor Tyutin face-first into the boards behind the Columbus net with 5:18 to play in the first.
The play saw Brassard and Cooke get into a fight afterwards and after the dust settled the teams skated 4-on-4 for the next two minutes. Columbus then had three minutes of power play time, but the team was unable to take advantage.
The second goal of the game went to Columbus. On the fly, R.J. Umberger let loose with a shot from the left circle that Fleury stopped, but the rebound kicked out front where it went off the skate of Pahlsson and went in. The play was reviewed to determine if Pahlsson kicked the puck in, but the goal was upheld and it was a 2-0 game 8:08 into the second.
With under three minutes to play in the second, Columbus made it a 3-0 game. Nash lifted the puck high into the air out of his own zone and it bounced right inside the blueline in the Pittsburgh end. Voracek caught up to the puck and was able to chip a backhander over Fleury for his 10th goal of the year.
Pittsburgh got on the board with a power play marker at the 7:29 mark of the third as Kennedy brought the puck to the left circle from behind the net and flung a wrister into the left corner.
The Blue Jackets, though, got their three-goal margin back six minutes later as a turnover in the Pittsburgh end resulted in a short 2-on-1 with Vermette finishing the break by following up his own rebound for his 13th goal of the year.
Pittsburgh hosts Los Angeles on Thursday... Columbus returns home to face San Jose on Wednesday...Pittsburgh had won four of five against Columbus coming into the game. Pittsburgh had also won three straight at home against the Blue Jackets prior to the loss...Umberger and Brassard each had two assists in the game...Pittsburgh forward Chris Kunitz was a late scratch due to a lower body injury. The team stated he is day-to-day.