Nyquist made it 1-0 14 seconds into the game by tipping in a shot from the point following Pierre-Luc Dubois' face-off win. It was the quickest the Blue Jackets have scored to begin a game this season.
"If he can keep leading the way, we'll follow him," Bjorkstrand said.
After scoring, Nyquist had an assist on Columbus' final two goals.
"After that first one, after our start there, we kind of lost our energy," Nyquist said. "But [Korpisalo] kept us in the game, and throughout the game he made some big saves."
Soderberg tied it 1-1 off a long rebound of Lawson Crouse's shot from the right point at 11:24 of the first.
Chychrun gave Arizona a 2-1 lead, taking Grabner's cross-ice pass and faking a slap shot from the left point before putting a wrist shot past Korpisalo at 12:04 of the second.
Bemstrom tied it 2-2, going behind the net to follow up his own missed shot and banking the puck off Kuemper's back on the power play at 17:36.
"I don't really care how it went [in]. That's a game-changer, to get it to 2-2," Bemstrom said of his first NHL goal. "Then [Bjorkstrom] gets the game-winner. It's a great start to the road trip."