Bourque had only two assists in four games before Tuesday.
"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."
Bourque and Iginla, who are tied for the team lead with 12 goals each, scored in the same game for the first time since Calgary beat San Jose 4-0 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. 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."
Lightning coach Guy Boucher was displeased with his team's effort, especially in the first period when the Flames took a 2-0 lead.
"It's extremely disappointing," 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."
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.
Stamkos said the Lightning have to force their opponents to take penalties to be successful. Tampa Bay had just two power plays against Calgary and failed to score on either.
"We haven't been really generating a lot of power plays especially on the road," he 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 took a 1-0 lead at 7:21 of the opening period when Sarich fired a point shot past Ellis for his first of the season. Calgary forward Tim Jackman screened Ellis on the play.
Kostopoulos put the Flames up 2-0 soon after when he swatted a loose puck at the side of the net past Ellis. Defenseman Mark Giordano took the initial shot from the point that Bourque tipped off the back boards. The puck came out front to Kostopoulos, who recorded his first point with the Flames in 11 games since being acquired from the Carolina Hurricanes.
"It's nice when it comes from somebody else, so our guys that are doing all the scoring don't have to do it all the time," Sarich said. "Usually when you can get some outside help from unusual sources things tend to work in your favor."
Bourque gave Calgary a 3-0 lead at 4:43 of the second when he cruised into the slot and converted a feed from Curtis Glencross to finish off a 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. 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."
The Lightning nearly tied it 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 a pass from Jay Bouwmeester past Ellis during a power play.
Sarich went 25 games since scoring his last goal, the game-winner in a 2-1 victory over Colorado in Denver on April 2. It was his only goal last season. ... Calgary D Steve Staios missed the game because of an upper body injury. D Adam Pardy got back into the lineup after missing 25 games because of a dislocated shoulder.
Copyright by STATS LLC and The Associated Press
Arena: Scotiabank Saddledome Location: Calgary, Alberta
Referees: Tom Kowal, Tim Peel Linesmen: Mike Cvik, Don Henderson
Attendance: 19,289 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Cory Sarich (1)
Assists: Adam Pardy, Brendan Morrison
Tom Kostopoulos (2)
Assists: Rene Bourque, Mark Giordano
Rene Bourque (12)
Assists: Curtis Glencross, Mikael Backlund
Johan Harju (1)
Assist: Pavel Kubina
Ryan Malone (8)
Assists: Nate Thompson, Victor Hedman
Jarome Iginla (12)
(Power Play) Assists: Jay Bouwmeester, Rene Bourque