The Penguins trailed 3-0 after two periods but came back to tie it before Picard scored with 2:02 to play for the Blue Jackets. But Kunitz answered 17 seconds later to send the game to overtime.
Less than a minute into overtime, Kunitz took a pass in the slot from Crosby, who had stolen the puck behind the net.
Mayorov scored twice in a span of 4:24 late in the second period.
The game was originally scheduled for Sept. 25 but moved back because Pittsburgh is hosting the G-20 summit of world leaders that day and traffic is heavily restricted around the city.
The Penguins just reported to camp Saturday -- two days after being honored at the White House by President Barack Obama. They went through only their third practice of training camp earlier in the day Tuesday.
Copyright by STATS LLC and The Associated Press
PITTSBURGH, PA - SEPTEMBER 15: Jakub Voracek #93 of the Columbus Blue Jackets attempts a wrap around against the...