Werenski gave the Blue Jackets a 4-3 lead at 13:37 of the third period with a power-play goal originally credited to Jenner before Chychrun tied it.
"You can give [the goal] to him, I don't want it," Werenski said. "I don't want it. He can take it."
The game was tied 1-1 until the Blue Jackets and Coyotes combined for four goals in 2:48 late in the second period.
Phil Kessel's 14th goal in 30 games against Columbus gave Arizona a 2-1 lead at 16:29, but Jenner scored his second goal of the game 23 seconds later to tie it 2-2 at 16:52.
Danforth, who made his NHL debut at age 28 Monday, scored the Blue Jackets' second goal in 43 seconds to make it 3-2 at 17:34.
An undrafted forward who signed with Columbus in May, Danforth is playing in his fifth league (NHL, American Hockey League, ECHL, Kontinental Hockey League and Liiga) in six seasons.
"To get your first goal in the NHL is obviously a big one," Danforth said. "It just felt like one of those nights. I was inches away from getting a couple of more."