After taking a feed from Olli Jokinen off the rush, Glencross took a couple strides before firing his 14th goal of the season past the glove of Corey Crawford at 8:37 of the third. Jokinen finished with two assists on the night.
After sitting outside the top eight in the West for exactly 100 days, the Flames move ahead of the idle Los Angeles Kings and into sole possession of the eighth spot. Calgary (27-21-7) is 7-0-1 in its last eight games and continues a four-game homestand Wednesday against the Ottawa Senators.
"It's a great accomplishment for us," Glencross said. "We put ourselves in a hole early in the year and we've bounced back. We've had some adversity and we've shown a lot of courage to come back."
Patrick Kane scored for Chicago (27-22-4). The defending Stanley Cup champions have lost four of their last five and sit tenth in the West. The Blackhawks are 1-2-0 halfway through a six-game road trip, which continues Wednesday in Edmonton.
"We're giving away points," said Chicago winger Troy Brouwer. "The way we're sliding right now, we've got to find a way to get out of it and get out of it real quick or we're going to find ourselves in a real big hole."
After backing up Marty Turco the past two games, Crawford was inserted back in the lineup and responded with an excellent effort. He stopped 20 of 21 shots to keep the game tied 1-1 after two periods with his best saves coming late in the frame.
Backlund took a pass from Alex Tanguay and ripped a shot from 15 feet out that Crawford got his blocker on. Moments later on a power play, Bourque's wrist shot deflected wildly and was going in before Crawford stuck out his leg.
Crawford also had some luck on that man advantage with Jokinen blasting a shot off the post. Earlier in the period, Jarome Iginla also hit the iron.
Chicago also hit a post with Brent Seabrook finding iron early in the third with the game still tied.
Chicago tied the game 1-1 at 5:56 of the second period on a tough shift for the Flames' top defence pairing.
Robyn Regehr was unable to contain Jonathan Toews along the boards and eventually he ended up with the puck behind the Calgary net. In the slot, Jay Bouwmeester got caught watching as Toews zipped a pass out to the wide open Kane and he fired his 15th past Kiprusoff.
Calgary grabbed the lead at 14:33 of the first thanks to a good shift from the fourth line. After crossing the Chicago blue-line, recent AHL call-up Lance Bouma threaded a perfect pass to Backlund, who beat Crawford with a nifty deke to his backhand.
"It was tough days in here, we lost a few too many games in the fall and we were struggling, but we never stopped believing in ourselves and we always kept working," Backlund said. "Lately we've been playing really good hockey consistently and it feels really good to be back in the playoffs again."
Chicago's top-ranked power play went 0-for-4, getting blanked for the second straight game. Calgary was 1-for-4 with the extra man.
"We needed pucks at the net, traffic at the net, and that was not anywhere near close enough to get it done," said Chicago coach Joel Quenneville. "I think we're better off with anger than frustration, but channeling it properly has got to be part of it. There was an undisciplined penalty at the end that we can't take."
Material from wire services and team media was used in this report.
1 - 0 CGY
1 - 1 Tie
2 - 1 CGY
PPG - EN -
3 - 1 CGY
Holding the stick
Interference on goalkeeper