Trailing 1-0 after two periods, Calgary tied it 1:28 into the third when Hudler scored on a two-on-one.
The goal came after Brodziak opened the scoring with 1:38 left in the second period, taking advantage of a turnover deep in the Flames' end when Iginla failed to get the puck out.
It was the first goal of the season for the 28-year-old, who was coming off a year in which he recorded career highs for goals (22) and points (44). This year has been a struggle. Brodziak entered the night with no goals, one assist and his minus-6 was better than only Suter's minus-7.
"Finally," said Brodziak, cracking a smile. "Hopefully they'll come more often. It's tough to explain sometimes when it's not going in. It's not something you can dwell on, you just have to focus on playing a strong game."
With Miikka Kiprusoff out with a lower-body injury, Irving's third consecutive start and 10th career start was also his first ever appearance at the Scotiabank Saddledome.
He didn't have long to settle his nerves as he was tested in the opening minute by Koivu, who pounced on Tanguay's giveaway but had his close-in shot turned aside by Irving. The 24-year-old goalie finished the game with 23 saves.
"I take pride in shootouts as a goaltender but it wasn't there tonight," said Irving, who was also beaten by Zach Parise on the first shot.
Notes: The Flames face Dallas on Wednesday. ... The Wild departed for Vancouver where they'll play the Canucks on Tuesday. ... Calgary dropped to 6-21 all-time in shootouts at home. ... Calgary D Cory Sarich played after sitting out the past four games. ... It was the first of five meetings between the two clubs, the first three coming in a 16-day span. ... Iginla has 35 goals against Minnesota in 67 career games. The only other team he has scored that many goals against is Colorado, but his 35 goals against the Avalanche have come in 89 games. ... Calgary played its 10th game of the season, the last NHL team to reach that mark.