Fabian Zetterlund looked to have scored at 13:49, but the goal was disallowed after video review confirmed the puck was batted into the net with his glove.
"I saw the guy kind of grabbed the puck with his hand," Zadorov said. "[Wolf] told me there was no goal. I'm like, 'Yeah, that's fine.' He was just, 'Yeah, there's no way it's a goal,' and we were fine."
Zadorov tied it 1-1 at 13:36 of the second period with a short-side shot by Kahkonen's blocker after Andrew Mangiapane redirected a Mikael Backlund pass cross-slot.
Kahkonen stopped Matt Coronato's wrist shot from 15 feet at 14:03 on a setup by Jakob Pelletier. Coronato, the No. 13 pick in the 2021 NHL Draft, was also in his NHL debut after signing with the Flames on March 26 following his sophomore season at Harvard.
"'Pelts' set me up for one through the legs. Unbelievable play," Coronato said. "He made a nice save. Just working hard and see what happens, but it was a great play by him."
Zadorov made it 2-1 at 4:01 of the third period on a wrist shot from the point over Kahkonen's blocker.
The goal came before Wolf, selected in the seventh round (No. 214) of the 2019 NHL Draft, made a glove save on Tomas Hertl's wrist shot at 11:41 and an arm save on Logan Couture's shot from the hashmarks at 14:39.
"Felt good," Wolf said. "I thought maybe a little shaky in the first period and I settled down. Not a lot of shots. Just tried to stay into it. Good third period. I was happy with that."
Zadorov shot into an empty net from his own zone at 19:00 for the 3-1 final, his second attempt at completing the hat trick with Kahkonen on the bench.
"I blacked out. I'm not going to lie," Zadorov said. "[Rasmus Andersson] told me to just go for it. First time it hit the D-man. Second time I just closed my eyes, kind of felt where the net was, got a lucky bounce. It was nice. Fade. Six-iron in there. It worked."
NOTES: Coronato, who had had 36 points (20 goals, 16 assists) in 34 games at Harvard this season, finished with four shots and a plus-1 rating in 14:38 of ice time. ... Zadorov's hat trick is the first for the Flames this season. … Wolf is 41-9-2 with a 2.08 goals-against average and .932 save percentage in 53 games with Calgary of the American Hockey League this season. ... Wolf (21 years, 362 days) is the fourth-youngest goalie at the time of his first win in Flames/Atlanta Flames history behind Trevor Kidd (20 years, 17 days), Pat Riggin (20 years, 227 days) and Dan Bouchard (21 years, 318 days). … Zadorov is the sixth defenseman in franchise history with a hat trick and the second with a natural hat trick (Paul Reinhart, Nov. 24, 1986). … Mangiapane has eight points (three goals, five assists) in his past eight games. … Sharks defenseman Jacob MacDonald played his 100th NHL game.