Calgary battered Chicago goaltender Corey Crawford to halt the Blackhawks' four-game winning streak.
Bourque scored his sixth of the season 40 seconds deep into the middle period to give the Flames a 2-1 lead. Paul Byron added a goal just 17 seconds later and Glenncross delivered his first of the contest with 8:56 left in the stanza.
Calgary took a 4-2 lead into the final period and Glenncross put a wrist shot past Crawford 6:46 into the third for the final tally.
The win went to Miikka Kiprusoff, who stopped 30-of-32 shots. Crawford allowed the five goals on just 26 shots.