Bourque's 23rd goal of the season came after he broke in alone on Jonas Hiller and put a wrist shot through the legs of the Anaheim netminder. Iginla set things up by stealing the puck from Corey Perry at his blue line and chipping it ahead to Bourque.
"Iggy and Perry fell down, so I knew as soon as I got the puck I had pretty much a clear breakaway from the red line out," Bourque said. "I just shot it five-hole and it went in."
With the score tied late in the period, Iginla's defensive hustle came at a critical time.
"It's 1-1, and Perry brought the puck across the blue line," Calgary coach Brent Sutter said. "We did a good job by not giving time and space. Jarome reacted quickly to him and was able to strip the puck away from him, and Bourquie was able to jump on it.
"That's a huge goal because now you go into the third period up one instead of being tied."
"Defensively, I thought we reacted well to situations," Sutter said. "I thought we did a good job of reacting properly and making sure our support was good in our zone."
Scott Niedermayer scored for the Ducks, who are nine points out of a playoff spot with 10 games remaining.
"We're obviously pretty disappointed," Niedermayer said. "We know the position we're in each night. Those two points are what we need each night. You've got to give the Flames credit, they played a pretty good defensive game and made it tough for us to get chances. I think we could have done more to create more chances and go to the net a bit more."
Calgary's Miikka Kiprusoff stopped 22 of 23 shots to earn his 32nd win of the season. Hiller made 25 saves for Anaheim.
With Daymond Langkow out of the lineup because of a neck injury sustained Sunday at Minnesota, the Flames called up forward Brett Sutter from Abbotsford of the American Hockey League.
It didn't take long for Sutter to make an impact. He dropped the gloves and fought Anaheim defenseman Brett Festerling two minutes into the first period, knocking his opponent down.
The Flames took a 1-0 lead on a fluky goal by Dawes during a Calgary power play at 15:11 of the first. With Dawes driving to the slot, Steve Staios let go a shot from the point that hit the Calgary forward and bounced into the net.
"We made a couple mistakes," Anaheim forward Saku Koivu said. "They got a lucky one there in the first on the power play and then they capitalized on the chances they got. It's a tough one to take."
Anaheim tied it at 14:27 of the second period when Niedermayer's point shot found its way into the top corner behind a screened Kiprusoff.
Following Bourque's late second-period tally, Hagman added an insurance goal early in the third when he converted a feed from Iginla for his first goal in 13 games. It was only his second in 18 games with the Flames after being acquired from the Toronto Maple Leafs in a seven-player deal on Jan. 31.
"I've been starting to feel a little bit better lately and getting a little bit more chances," Hagman said. "Right now you just try to battle and try to go for the net and hopefully get some pucks in. I was pretty happy to get one. It's been a stretch without goals. Hopefully, now I can help the team a little bit more by scoring goals."
The Flames are 30-1-3 when leading after two periods and 29-11-6 record when scoring first this season. ... The Ducks are 18-11-1 since Jan. 5 ... Hiller has started 18 consecutive games and 29 of 30 for the Ducks.
Copyright by STATS LLC and The Associated Press
Arena: Scotiabank Saddledome Location: Calgary, Alberta
Referees: Marc Joannette, Dan Marouelli Linesmen: Mike Cvik, Brian Mach
Attendance: 19,289 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Nigel Dawes (12)
(Power Play) Assists: Steve Staios, Jay Bouwmeester
Scott Niedermayer (9)
Assists: Matt Beleskey, Todd Marchant
Rene Bourque (23)
Assist: Jarome Iginla
Niklas Hagman (22)
Assists: Jarome Iginla, Jay Bouwmeester