The goal was his first of the playoffs.
"Yeah, I mean it's the most fun. It's why we play, is for the playoffs," said Bozak.
"Obviously an exciting building. The crowd was awesome. Obviously we were nervous at the start, but I thought we found our game as the game went on. I thought everyone did a great job," he added.
David Perron, who scored the other St. Louis goal on the night, said told Bozak he wasn't going to miss another scoring chance.
Bozak was stymied by Hellebuyck with about seven minutes left in the third after being setup by teammate Zach Sanford.
"It's funny, I told Bozie right before his shift, I said, 'You're not going to miss again,' because he missed two chances before that. I said, 'You're not going to miss three times,' and he buried that one high blocker, I think, so that was awesome for us."
Perron's tally, just over four minutes into the third tied the contest at one.
Jordan Binnington turned aside 24 shots for St. Louis.
Connor Hellebuyck made 24 saves for Winnipeg.
Patrik Laine's goal scored 13:28 into the opening period of the series was the lone goal for the Jets on this night.
Bryan Little scooped up a puck to the right of St. Louis goaltender Jordan Bennington before hitting Laine in the high slot.
The 21 year-old Finn wired a wrister past him to score his first goal of the playoffs.
"We had a pretty solid game. We lost their guys in the third a couple of times and they got some good chances. They were able to score two, but overall, for two periods we played some good hockey. It’s a frustrating loss, but we’ve got to focus on Game 2," said Laine.
There was no scoring in the second period.
The Blues pushed back early in the frame but Winnipeg goaltender Connor Hellebuyck was equal to the task, stopping Vladimir Tarasenko on a breakaway at 4:45.
Dustin Byfuglien came close to giving the Jets a lead on the power play late in the period when hit a goalpost with 1:20 left on a slapshot from the point.
Patrik Laine nearly made it 3-1 early in the third when he hit the goalpost off a wrist shot.
St. Louis tied the contest 4:05 into the third period when David Perron took a backhand pass from Colton Parayko before beating Hellebuyck through a screen with a nearly 60 foot wrister to make it 1-1.
Mark Scheifele nearly tied the contest with 12.4 seconds left with an extra attacker on a one timer but Bennington kicked out his right pad before lying on the puck to snuff out the Jets scoring chance.
"They (Jets) were moving the puck around. It went down to Scheifele and I had to make a little bit of a desperation save there and hope for the best, with the boys coming and clearing out the rebound. That's all I remember. And we're happy with that win," said Binnington.
Blues Head Coach Claude Berube was pleased with the win and said he wasn't surprised by the way it was played.
"They just stayed with it. I thought … we kind of had the same game plan all 60 minutes tonight. I thought that we were pretty solid. You know, both ways, they were good, too. They gave us some trouble. Laine hit the post there the one time, but overall, we were pretty solid all 60 minutes and played our game. Power play was just OK, could have got a few more looks there, but they did a good job killing. It was a hard game, just as we expected."
Jets Head Coach Paul Maurice's take on the game was simple.
"PK was real good. It was good playoff hockey. It wasn’t an open game, and none of them are going to be. It’s not breaking loose in this series. It’s going to look almost like that right through. Just take one or two of their chances away from them a night, the ones you think you can clean up, and then make good on yours."
SHOTS-ST. LOUIS 26 WINNIPEG 25
Game 2 goes Friday in Winnipeg.