The win extended the Coyotes' winning streak to three games and gave them their first sweep of a season series with the Flames in nine years.
Yandle and Rozsival scored in the first 2:12 of the third period to extend the Phoenix lead to 4-1. The Flames cut the lead to 4-3 in the next 7:16 on goals by Mikael Backlund and Alex Tanguay.
Ilya Bryzgalov held on the rest of the way in goal for the Coyotes and finished with 24 saves. Lee Stempniak and Eric Belanger scored the first two Phoenix goals.
Olli Jokinen also scored for the Flames, who lost their third in a row but held on to the eighth playoff spot in the Western Conference. Miikka Kiprusoff allowed four goals on 25 shots.