The season-high five-goal output was a relief for the Flames after they managed just one goal in five of their previous eight.
Calgary improved to 5-0 when scoring four or more goals. Lee Stempniak, Rene Bourque and Paul Byron also scored for the Flames.
Defenseman T.J. Brodie, called up from the AHL on Nov. 9, got his first NHL point by assisting on Stempniak's goal.
Viktor Stahlberg and Marian Hossa had the Blackhawks' goals. Miikka Kiprusoff made 30 saves on 32 shots for the win.
Chicago's Corey Crawford stopped 21 of 26 in the loss.
Calgary scored twice in a 17-second span at the start of the second period to take a 3-1 lead. The Blackhawks reduced the deficit with a power-play goal, but Glencross restored Calgary's two-goal cushion heading into the third.
The Blackhawks couldn't score on a two-man advantage with 2:45 remaining in the game.