Johnny Gaudreau and Mark Giordano each had two assists for the Flames (18-9-2), who have won four in a row and are 8-1-1 in the past 10 games.
"You always want to win every game," Lindholm said. "Minnesota played a good game. Smith] made some huge saves for us at key moments, so we have to thank him for this one."
***[WATCH: [All Wild vs. Flames highlights]*
Smith got his second shutout of the season and 38th in the NHL. He has won five straight after six losses in his previous eight games.
"It's easy to say you're back, and then the next game, anything can happen," said Smith, who has a 1.50 goals-against average and .939 save percentage in his past five games. "I think you've got to take it one day at a time and not get too far ahead of yourself and not ride the roller coaster. It's easier said than done, but when things are going well, you don't want to take it for granted."
Alex Stalock made 18 saves for the Wild (15-11-2), who have lost four of five.
"I thought we were good again," Stalock said. "It's been three games in a row where we've played good, honest hockey. We're just not getting bounces right now, I think."
Lindholm put Calgary ahead 1-0 when he took a pass from Gaudreau on a 2-on-1 50 seconds into the second period.
Lindholm made it 2-0 when he scored on a cross-slot pass from Gaudreau at 1:13 of the third period.
"The first one, I think he slid out of the net. So the second time, I knew he kind of was aggressive, so I just tried to freeze him for a little," said Lindholm, who had a goal at 13:16 of the first period overturned after Minnesota coach Bruce Boudreau challenged for offside. "It was nice to see it go in and nice to get this one."
