Kiprusoff has not allowed a goal in 99:01 and has given up only one in his last three games, all victories, to help the Flames improve to 7-7-2.
The teams will meet again Monday night in Calgary.
"Fortunately we've got a chance here to rebound on Monday," Vancouver captain Marcus Naslund said. "We didn't get in close enough to really test Kiprusoff."
Alex Auld stopped 26 shots for the Canucks in his first loss of the season.
"The guy at the other end stood on his head and played amazing," Auld, who dropped to 5-1-1. "Obviously I wasn't going to win every game all year and go undefeated."
Nilson scored midway through the first period off a pass from Craig MacDonald, wristing a perfect shot over Auld's glove and under the crossbar. Nilson also scored the winner in the Flames' 2-1 victory over Columbus on Thursday night.
"The pass was just a rocket, so it gave me a lot of time to shoot it," MacDonald said. "That's the way it is. Sometimes nothing goes in and sometimes you're in the right spot."
MacDonald's assist was his first point in six games with the Flames.
"I threw a pass out front to him and he made a great play to finish it," MacDonald said. "It's exciting to get my first point as a Flame."
Right after Nilson's goal, Canucks defenseman Wade Brookbank fought with Flames forward Darren McCarty. Vancouver's Jarko Ruutu earlier squared off with Calgary's Byron Ritchie, and Nilson later tangled with Trevor Linden.
- The Flames were 1-7-2 in their previous 10 games against the Canucks at the Saddledome.
- Vancouver is 10-3-2.