The Dallas Stars already experienced that in the past few days.
The rookie goaltender is expected to get a fifth straight start as he tries to lead the Wild to another win over the fading Stars on Tuesday night.
Minnesota (27-19-5) has won seven of nine games despite being without Parise (broken foot) and Koivu (ankle surgery). Parise has been out for 13 games and is expected to miss at least one more, while Koivu -- the team leader with 35 points -- may be out for two more weeks.
Kuemper, meanwhile, is spurring the Wild, going 4-1-0 with a 1.37 goals-against average in five games since being recalled from Iowa of the AHL after Josh Harding fell ill.
"When things are going well, the game's a lot of fun," Kuemper told the team's official website. "Obviously, I've always dreamed about playing in the NHL so now I'm getting a chance to do it and it's been a blast."
He's likely to start ahead of both Harding and Niklas Backstrom for a fifth straight game after winning the last two while stopping 53 of 56 shots.
"We're giving him more opportunities because he's taking advantage of those opportunities," coach Mike Yeo said of the 2009 sixth-round draft pick. "We're very fortunate to have a guy like that come in and perform at the level that he's played at, and do it with confidence.
"Sometimes your third goalie is called upon to back up or play a game here or there. But certainly he's been thrown into more of a starting role for us and he's taken that opportunity."
Kuemper was superb again Saturday, making 33 saves in a 3-2 overtime win over Dallas (21-20-8). Defenseman Nate Prosser scored in the extra session after rookie Erik Haula got his first career tally in the opening period.
Prosser has a goal in each of the last two games after getting one in 73 over his first four seasons.
"When you're playing the right way, it is going to be a different guy every night," Yeo said.
Minnesota has won four of the past five meetings with the Stars, including both this season. However, the Wild fell 5-3 in the most recent at Dallas on March 29.
The Stars are in a tailspin, having dropped nine of their last 10 after Monday's 4-1 loss at Nashville. They gave up the final four goals after Cody Eakins' first-period power-play goal.
"I'll take the blame for that," captain Jamie Benn said of Dallas' latest dismal performance. "When you're a leader, it's unacceptable. I think for myself, it just wasn't being smart with the puck. We talked about it, but I'm still doing it. It's something I have to clean up and the rest of the guys do too."
Tyler Seguin also shoulders some of the blame, as he's gone nine games without a goal. The center still leads the team with 21 goals and 24 assists, getting a point against the Wild on Alex Chiasson's tally.