Vasilevskiy made 17 saves in his surprise start against the Chicago Blackhawks and allowed two goals in the Lightning's 2-1 loss that tied the series.
"That's a hell of a job in my book," Cooper said. "That kid gave us every chance to win the hockey game. ... He showed at the pinnacle of the sport that he can play."
The Lightning called Bishop day-to-day with an undisclosed injury. Cooper said Bishop will play again in this series "no question" but doesn't know in what game.
There are two days off before Game 5 Saturday, which gives Bishop some extra time.
But Wednesday night it was Vasilevskiy's show as Latvian Olympic hero Kristers Gudlevskis backed up. The 20-year-old Russian didn't face a shot for more than eight minutes and only saw two the entire first period.
"We'd like to test him a little more than that, no question," Blackhawks winger Patrick Sharp said. "Two shots wasn't the way we wanted to draw up the period."
Vasilevskiy allowed one goal as Jonathan Toews crashed the net and another when Brandon Saad got a backhander past him. But no one could blame him for the Lightning's loss.
"It's my dream to play in the Stanley Cup final," Vasilevskiy said. "I think I look not bad in my first game in two months. I can play better, for sure, but for the first time, not bad."
Since Bishop was injured and had to leave Game 2, the Lightning have boasted of their confidence in Vasilevskiy, one of the top goaltending prospects in hockey. Cooper said this performance validated that confidence, and Vasilevskiy's teammates were proud of how he stepped in.
"That's all you can ask for in a goalie being put in that situation," captain Steven Stamkos said. "He stepped up, made some big saves, and we had a chance."
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