Vasilevskiy made 73 saves in his three straight shutouts and 91 in a shutout streak that spans 10-plus periods.
He hasn't allowed a goal since Carolina Hurricanes forward Jesper Fast scored on the power play at 19:15 of the second period on Feb. 22.
Vasilevskiy made 25 saves in a 3-0 win against the Hurricanes on Feb. 24, 20 saves in a 5-0 win against the Dallas Stars on Feb. 27, and 28 saves in a 2-0 win against the Stars on Tuesday.
"It's one of those times in your playing career where you just feel great, your timing is on, you're seeing the puck well and your reads are impeccable," Boucher said. "[Tuesday against Dallas], he caught a break, that one where Jamie Benn shot it, it ricocheted off his arm and rib and stayed out. I mean, that could have easily gone in, so you're getting the breaks and it's a nice feeling. You don't know how long it's going to last, so you always have that in the back of your mind. But there's no doubt that you're riding a wave of confidence knowing you haven't given up a goal in a long time."
The longer it goes, the harder it's going to be for Vasilevskiy to keep his focus off the streak and the records he's chasing, said Boucher, who didn't realize the attention his streak was getting until after his fourth straight shutout.
"All of a sudden you started to really think about it," he said. "Before you were just riding this really fun wave of confidence. You weren't thinking about too much other than going out there feeling great about your game and your team. Then you get to four and you start thinking, 'Oh, jeez, we're this far away from a record.' It starts to cloud your judgement."
Boucher said his Coyotes teammates were relieved when he finally allowed a goal, to Randy Robitaille of the Atlanta Thrashers, to end the streaks.
"In some ways I was [relieved] too," he said. "I'm glad it ended after we got the record, but at a certain point you have to resume normal life and that's going out trying to win a hockey game, not necessarily trying to get a shutout."
Vasilevskiy doesn't need to break Boucher's records to validate his NHL credentials. He helped the Lightning win the Stanley Cup last season, and was voted winner of the Vezina Trophy as the best goalie in the NHL in 2019-20.
Boucher said he thinks Vasilevskiy is the best goalie in the NHL right now and the unquestioned favorite to win the Vezina again this season with his 13-3-1 record, 1.65 goals-against average, .942 save percentage and, at least for now, three shutouts in 17 games.
"You can give him the first, second and third (place) votes for the Vezina," Boucher said. "Just from a pure talent standpoint he is the best goalie in the League. Whether he wins the Vezina or not, nobody matches up to his capabilities in net. No chance. Some people have talent and never live up to the expectations. He's living up to the expectations. We're not clamoring for more. We're wondering if he can get more, but we're not clamoring for it. We see greatness."