Carl Soderberg made it 2-0 on a 2-on-1 with Crouse at 8:22 of the second.
"Other than [part of the second period] it was a tight game, and it's been that way for however many games," Flames forward Matthew Tkachuk said. "That's kind of a [Stanley Cup] Playoff style; they're tight games, and you're not going to get a ton of chances each way."
Crouse scored into an empty net with seven seconds remaining for the 3-0 final.
"That 2-0 lead made it a tough climb," Calgary coach Bill Peters said. "We had some good looks, but we just couldn't find the net."
Kuemper's shutout was his second of the season and the 18th of his NHL career, coming in his 200th NHL game. He is 4-1-1 against the Flames.
"We've been talking a lot about getting back to being a little bit tighter," Kuemper said, "and I thought the guys did a great job, blocking a lot of shots and keeping guys to the outside to let me see the puck."