Bourque had a goal and two assists as the Flames beat the Tampa Bay Lightning 4-2 at Scotiabank Saddledome.
Cory Sarich, Tom Kostopoulos and Jarome Iginla also scored for the Flames (12-14-2), who now play back-to-back games in California against the Los Angeles Kings on Thursday and the Anaheim Ducks on Friday.
"We've got to keep this going," Bourque said. "If we are not putting a few wins together and we are just kind of staying at the bottom, we're not really moving and we're not really catching anybody. We're still close and we have time but we can't just keep saying next game, next game."
Johan Harju and Ryan Malone replied for the Lightning (15-10-3), who were coming off a wild 6-5 win over the Colorado Avalanche at home on Saturday.
Calgary goalie Miikka Kiprusoff stopped 22 shots, while Dan Ellis made 15 saves for Tampa Bay.
Lightning forward Steven Stamkos was held without a goal for the sixth straight game. He scored 21 goals in his first 22 games. Stamkos has also gone three games without a point.
"We haven't been really generating a lot of power plays especially on the road," Stamkos said. "It's something that obviously is part of our game plan that we're not doing. We're not getting first on the puck. We're not forcing them to take penalties. That's costing us by not getting on the power play that much."
The Flames opened the scoring at 7:21 of the first period when Sarich blasted a point shot past a screened Ellis for his first goal of the season.
Kostopoulos put the Flames up 2-0 a short time later when he swatted a loose puck at the side of the net past Ellis. Mark Giordano took the initial shot from the point that Bourque tipped off the back boards out front to Kostopoulos, who recorded his first point as a Flame in 11 games since being acquired in a trade from the Carolina Hurricanes.
"It's extremely disappointing," Tampa Bay coach Guy Boucher said. "To me it's a wasted first period. Even if we do come back, it doesn't excuse our first period and it doesn't make us worthy of winning this game."
Bourque gave Calgary a 3-0 lead at 4:43 of the second period when cruised into the slot and converted a feed from Glencross to finish off a nifty three-way passing play.
The Lightning rallied with goals by Harju, the first of his NHL career, and Malone before the end of the second period. Harju snapped a shot that found its way through Kiprusoff's legs, while Malone parked himself beside the net before swatting a pass from Nate Thompson into the top corner.
"We didn't crack, we stayed with it," Calgary coach Brent Sutter said. "They've got a quick team and they come at you really hard, especially in the second."
The Lightning nearly tied the game early in the third period but Kiprusoff stood his ground to stop a wraparound attempt by Thompson before denying Martin St. Louis on the rebound attempt.
Iginla then put the game away when he one-timed pass from Jay Bouwmeester past Ellis during a Calgary power play.
It's the first time that Bourque and Iginla, who are tied for the team lead with 12 goals each, have scored in the same game since a 4-0 road win against the San Jose Sharks on Oct. 24.
"If we're both scoring that means both lines are playing well and our top six forwards are getting the job done and producing and that's what we need," Bourque said. "If we can keep this going together and more often I'm sure it's going to result in more wins."
Material from wire services and team media was used in this report.