Jarome Iginla was tripped by Phaneuf on a breakaway with less than 2 minutes left, but Gustavsson stopped the Flames' captain on the ensuing penalty shot.
Phaneuf, the Maple Leafs' captain, played his first game at the Scotiabank Saddledome since the Flames traded him to Toronto in a multiplayer deal Jan. 31.
His return coupled with Toronto's only visit of the season led to a hyped build-up. There were dozens of Maple Leaf jerseys in the Saddledome and chants of "Go Leafs Go!" went up before players stepped on the ice for warmups.
But the two players still with Calgary from that trade made a bigger impact in this one. Hagman had a goal and an assist and Matt Stajan added an assist.
"It's obviously nice beating the blue and white where I was for so long," Stajan said. "We went back-to-back finally. We can start climbing now. It's a big confidence boost for our team."
There wasn't much to get excited about for either side until the Flames broke loose for three goals in 57 seconds starting at 15:17 of the second period. Tanguay, Jokinen and Bourque scored in succession to give Calgary a 4-1 lead heading into the third.
Phaneuf was greeted jeers and a few cheers when he touched the puck on his opening shifts, but it was a strangely quiet game from a player known for his punishing checks and laser shots from the point.
The 25-year-old attended his grandmother's funeral on Prince Edward Island on Wednesday and arrived in Calgary later that night.
"It wasn't a great day yesterday, by any means," Phaneuf said. "It's tough. It's emotional to go to those things, but it was a good celebration of her life and I'm glad I got to it and I have no regrets of going whatsoever."
Calgary's power play, which was ranked 24th in the NHL, managed two goals on three opportunities.
Grabovski scored Toronto's second goal at 8:45 of the third. His slap shot from two strides over the blue line beat Kiprusoff over the left shoulder.
Hagman scored the second of Calgary's power-play goals at 2:30. Jokinen flipped the puck from the blue line to Hagman in the high slot and the Finn scored with a high wrist shot.
"Obviously, I wanted to win, too. I wanted to play well against my old team and show them that I can still play," Hagman said.
The Flames chased the opposition's starting goalie for the second straight game. Blue Jackets netminder Steve Mason was replaced in the first period Monday after giving up two early goals.
Tanguay gave Calgary a 2-1 lead at 15:17 of the second. He beat Giguere glove side on Stajan's feed from the end boards.
Stajan, who turns 27 next week, was the key player in the Phaneuf deal for Calgary. The start of his season was delayed by a shoulder injury and he has only one goal in 26 games. He was a healthy scratch in Calgary's two previous games.
With Grabovski serving a minor for tripping, Jokinen added to the Calgary lead with a slap shot from the top of the faceoff circle at 15:50.
Jokinen then shoveled the puck up to Bourque in the neutral zone and once the winger gained the offensive zone, he unleashed a shot to beat Giguere's glove at 16:14 of the second for a 4-1 lead.
"They finished their scoring chances and we weren't very good for two periods," Toronto coach Ron Wilson said. "They beat us in races to pretty much every puck -- in our zone and their zone, too."
Kotalik was playing his sixth game this season after missing 26 with a knee injury. ... With his assist on Tanguay's goal, Iginla extended his point streak to nine games (five goals, seven assists). ... Calgary sent Phaneuf, forward Fredrik Sjostrum and defenseman Keith Aulie to Toronto for Stajan, Hagman, forward Jamal Mayers and defenseman Ian White. Mayers signed with Tampa Bay in the offseason and White was dealt to Carolina in November. ... Calgary's three-goal burst was the seventh-fastest in franchise history.
Copyright by STATS LLC and The Associated Press
Arena: Scotiabank Saddledome Location: Calgary, Alberta
Referees: Greg Kimmerly, Brad Meier Linesmen: Brad Lazarowich, Brian Mach
Attendance: 19,289 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Nikolay Kulemin (10)
Assists: Clarke MacArthur, Francois Beauchemin
Mikael Backlund (4)
Assist: Brendan Morrison
Alex Tanguay (9)
Assists: Matt Stajan, Jarome Iginla
Olli Jokinen (5)
(Power Play) Assists: Anton Babchuk, Niklas Hagman
Rene Bourque (13)
Assist: Olli Jokinen
Niklas Hagman (8)
(Power Play) Assists: Olli Jokinen, Anton Babchuk