The plucky Kazakhs, who also got shootout goals from captain Roman Starchenko and Curtis Valk, have now won two straight shootouts for four points in the standings. In their Group B opener, they topped host Latvia 3-2.
Finland outshot Kazakhstan 51-20, including a 15-1 gap in the scoreless first period.
"We’re feeling pretty good," said Kazakhstan's Curtis Valk. "Both games were hard-fought games and our goalie [Nikita Boyarkin] obviously played amazing today. We’re going to need that going forward, but we stuck to the game plan, and that let us be successful tonight."
In regulation time, Anton Lundell, Finland's youngest player at age 19, scored his first Worlds goal. Kirill Panyukov got the other goal for Kazakhstan.
"It was a big win and a very emotional one," said Panyukov. "We all believed in ourselves and each other, and the coaching staff helped prepare us to play our best. That’s the way we did it. It was a big moment for us, and I believe we will have more big moments in this tournament."
The Finns gave up points in the standings for the first time since a 4-2 regulation loss to Germany in 2019 to wrap up the preliminary round.
"It was a tough game," said Finnish captain Marko Anttila. "I think they defended well and we had a lot of scoring chances, but we only scored one goal and they had a very good goalie. It's a little bit frustrating right now, but we know what we need to do better, and we just have to score goals when we get the chance."
In net, Harri Sateri, who was Finland's starting goalie at the 2017 and 2018 Worlds, had a far quieter night in his 2021 debut than the Worlds rookie Boyarkin, who shone in his second straight game.
With great hands and persistence, Lundell opened the scoring for Finland at 13:24 of the second period. Going to the net, he got the puck off Petteri Lindbohm's shot, put his first shot off the right side of Boyarkin's cage, and then tucked in the rebound.
Seated next to Lundell at the post-game press conference, Anttila said: "It's very nice. It was a big goal for us at that moment. He has talent. You can see it. [To Lundell] Are you 19? Yeah, very talented guy."
Lundell, who won gold at his first World Juniors in 2019 in Vancouver, captained Finland to U20 bronze in Edmonton back in January. The first-round pick of the Florida Panthers (2020, 12th overall) had 16 goals and 25 points in 26 games for HIFK this season.
The Finns showed their trademark grit or "sisu." Forward Iiro Pakarinen doubled over in pain and skated to the bench after making a huge shot-block on Dmitriy Shevchenko’s blast. But they weren't converting on their offensive opportunities, as Boyarkin remained cool and poised.
It took just 18 seconds for Kazakhstan to tie the game on its first and only power play of the game. With Petri Kontiola off for hooking, Panyukov deftly tipped in Mikhailis's nice centering feed from the left faceoff dot at 15:56.
The Kazakhs pressed for the go-ahead goal as time wore on. With about 10 minutes to go in the third, Sateri, who earns his living with the KHL's Sibir Novosibirsk, stretched out his right pad to foil Panyukov on a breakaway.
The Finns bombarded Boyarkin with heavy traffic in front with under three minutes remaining. The ice opened up for 4-on-4 play with Jere Innala and Kazakhstan's Viktor Svedberg sent off for rough stuff with 2:36.
In overtime, the Finns controlled most of the play. After Kazakhstan mounted a late flurry around Sateri's net, Lundell and Mikael Ruohomaa narrowly missed connecting on a 2-on-1 rush.
The Kazakhs lost all three previous World Championship meetings with Finland (4-0 in 1998, 4-1 in 2012, 4-3 in 2014).
Both sides get a day off before resuming action on Tuesday. Finland takes on Norway, while Kazakhstan faces Germany.
"I think we've already improved a little bit in our defensive game and how our unit is playing together," Anttila said phlegmatically. "We have to keep on that way and of course be more effective in the offensive zone, screening the goalie better and getting better results. That's the key to winning the next game."