Brad Richards #91 of the Dallas Stars is out indefinitely with a spiral fracture in his left hand.
Glencross converted in the third round of the shootout after notching regulation winners in the previous two games, giving the Flames a 4-3 victory over the Dallas Stars on Wednesday night.
"We have confidence in Glennie," said Calgary's Alex Tanguay, who converted in the first round. "We knew he was going to score."
Glencross watched how goalie Kari Lehtonen reacted in the first two rounds and adjusted accordingly, scoring on a snap shot low to the stick side to give the Flames the extra point.
"He dropped down low on (Tanguay) and left the glove wide open," Glencross said. "The second one he kind of stood up a little more. The third one, he stood right up on me and took away everything high so I had to change my game plan and go somewhere else. It worked out for me."
After Tanguay scored in the second round, Dallas' Mike Ribeiro evened the shootout on a nifty move in the third round, setting the stage for Glencross.
Rene Bourque, Tom Kostopoulos and Anton Babchuk scored first-period goals during a 3:15 span to get the Flames off to a fast start before the Stars rallied.
Miikka Kiprusoff stopped 31 shots to help the Flames move into a fourth-place tie with Chicago in Western Conference, a point ahead of Dallas. Calgary has won three straight and is 8-2-1 in its last 11 games.
They left for a game Thursday night at Phoenix in a positive mood despite wasting the three-goal lead.
"For us it's all about getting points," Tanguay said. "We wish we wouldn't have given 'em one, but we're happy with the result."
Jamie Benn and Ribeiro notched regulation goals for Dallas, and Tomas Vincour drew the Stars even at 3 at 5:39 of the third period on a sharp-angled shot from the left circle for his first NHL goal.
Lehtonen made 31 saves for the Stars, 5-0-2 in their last seven and returning from a 3-0-1 trip.
"It's a positive point, given that we came back from a three-goal deficit, it's not often that you do that," Stars coach Marc Crawford said. "I'm sure we would've liked to have two points, but it was a good, hard comeback by our guys, they dug deep as they've done all year, and at this point, it's about getting all the points you can get, and tonight we managed to find a way to get one."
Calgary gained early momentum when Bourque fired a loose puck from the left circle past Lehtonen at 10:26 of the opening period.
The Flames needed only 1:02 to extend the lead when Kostopoulos capitalized on a rebound.
Babchuk's shot from the right point went in off Lehtonen's glove to make it 3-0 at 13:41 of the first period before Benn made it a two-goal game on a power play at 18:28.
Dallas dominated the second period with a 15-4 shots advantage and Ribeiro pulled the Stars within a goal on a wrist shot from the right circle at 5:12.
"We got a little off track there in the second," coach Brent Sutter said.
Stars center and leading scorer Brad Richards returned after missing 10 games with concussion-like symptoms. Richards was injured when he was hit in the head on a check in the closing seconds of a game against Columbus on Feb. 13.
NOTES: Benn has one goal in each of his last five games. ... The Flames scored on their second and third shots of the night. ... Stars D Nicklas Grossman (hip) missed his 11th consecutive game, but he's been practicing and could be active for Friday night's home game against Minnesota. ... The Flames were without C Brendan Morrison (knee), D Adam Pardy (shoulder) and C Daymond Langkow (neck).