Mikael Backlund and Michael Frolik each had a goal and an assist, and Elias Lindholm and Rasmus Andersson each had two assists for the Flames (36-16-7), who have won two in a row following a four-game losing streak (0-2-2) and lead the San Jose Sharks by one point for first place in the Western Conference.
"I think our team has realized what it's going to take down the stretch here to get two points," said Smith, who started three games in a row for the first time since Oct. 25-29. "Tonight was another big instance of it. I think it's exciting. Everyone's happy in here when we get two points."
WATCH: [All Coyotes vs. Flames highlights]
Conor Garland and Jordan Weal scored, and Calvin Pickard made 28 saves for the Coyotes (26-28-5), who have lost two of their past three games and remain three points behind the Minnesota Wild for the second wild card into the Stanley Cup Playoffs from the West.
"Right now our goal should be getting above .500 and then it should be getting to 10 games above .500," Weal said. "You've got to get to 90 points, 92 points. I think it's going to be the line this year, especially with how tight it is on this side (Western Conference). If we can get to that 92 points, then you're going to give yourself a good chance."
Austin Czarnik put Calgary ahead 3-2 at 16:47 of the second period with a low shot from the slot. He has scored in consecutive games after being a healthy scratch the previous nine games.
Frolik extended the lead to 4-2 lead at 5:48 of the third period, scoring from just outside the crease following a turnover by Coyotes defenseman Niklas Hjalmarsson, and Backlund scored into an empty net at 18:48 to make it 5-2.