The Flames won their fifth straight, a streak that has boosted their post-season hopes.
With teams around the league heading into their final 10 games of the campaign, Phoenix missed a chance to draw even with Dallas for the lead in the Pacific Division.
Coyotes and Colorado both have 81 points, leaving them tied for the seventh and eighth spots in the playoff chase. Calgary has climbed within one point of those two clubs.
Baertschi's goal put Calgary in front to stay and the Flames expanded their advantage early in the second period on the 31st of the season from Jarome Iginla.
Oliver Ekman-Larsson brought Phoenix within one late in the second, but Matt Stajan restored the two-goal lead less than a minute later.
A shorthanded goal from Calgary's Alex Tanguay in the third wrapped up the scoring.
Celebrity Families of 2014 [PHOTOS]