Dube ended Calgary's see-saw battle with the Columbus Blue Jackets at 2:25 of extra time for a 4-3 victory.
Gaudreau had two assists, missed a penalty shot and was constantly razzed by Flames fans in his first game in Calgary since departing for Columbus as an unrestricted free agent last July.
"The fans are very passionate. They are care a lot about our team and that's what they showed tonight," Dube said. "They care a lot about us, so we appreciate that. Felt really good to win for them tonight."
Calgary led 2-0 and 3-2 in the second period, but the Blue Jackets would not go quietly.
Mangiapane had a goal and two assists, and Walker Duehr and Nazem Kadri also scored for the Flames (23-16-9).
Calgary goaltender Dan Vladar stopped 21 saves for his second win in as many starts, while Columbus counterpart Joonas Korpisalo had 45 saves in the loss.
Gaudreau, who ranks fifth all-time in Flames franchise points with 609, was greeted by boos and derisive chants of "John-ny" the moment he stepped on the ice.
"We knew it was going to be that kind of environment. Johnny had an excellent game," Blue Jackets head coach Brad Larsen said. "The guys battled. We had some puck management issues, no question."
Gaudreau was awarded a penalty shot five minutes into the opening period when Calgary defenceman MacKenzie Weegar hooked him on a breakaway.
A wave of boos followed the left-winger's approach to the net, and intensified when he shot the puck high attempting to pick the net's top corner.
A video tribute minutes later brought many in the crowd of 17,697 to their feet to acknowledge Gaudreau's eight seasons of Flames' service, but that goodwill was short-lived.
"I think that just shows how good of a player he was and how important he was for this organization, because you don't get a reaction like that if you're not that important," Dube said.
The Blue Jackets were called for too many men with just over six minutes remaining in regulation, but Calgary didn't turn the advantage into a go-ahead goal.
"I'll let you look at it. You tell me that's too many men, I'll buy you lunch," Larsen said.
Jenner knotted the score 3-3 at 4:34 of the third period when he opted to shoot on a two-on-one with Gaudreau.
Trailing 2-0, Columbus tied the game midway through the second period with two power-play goals in a 49-second span before Mangiapane pushed Calgary ahead again at 16:17.
The Blue Jackets' power-play showcased Gaudreau's puck-distribution skills. He feathered the puck across to Laine, who dropped to his knee to squeeze a shot by Vladar at 9:53 of the second period
Marchenko scored when he ripped Gaudreau's cross-ice pass over Vladar's glove at 9:04.
"Looch's fight for sure got us back going the way we needed to," Dube said.
Kadri's team-leading 19th goal put Calgary head 2-0 by 1:32 of the second period. The Flames' celebration of Duehr's goal at 16:18 of the first period was delayed.
His one-timer from just above the faceoff dot deflected off the inside of Korpisalo's pad so fast that it was unclear where the puck was until officials fished it from the back bottom of the net.
Duehr, who was called up from the AHL's Wranglers for the first time this season on Jan. 7, has two goals in six games.
Flames defenceman Chris Tanev left the game midway through the first period after a neutral zone collision.
The Flames have earned at least a point in Vladar's last 12 starts, with a 9-0-3 record since Nov. 29. That's the longest active point streak this season among NHL goalies.
The Blue Jackets have played six rookies their last 16 games with a half-dozen regulars on injured reserve, including Jakob Voracek (concussion) and Zach Werenski (torn labrum) out for the season.
Columbus continues a four-game western road trip Wednesday against the Edmonton Oilers. The Blue Jackets are 3-16-1 on the road this season.
This report by The Canadian Press was first published Jan. 23, 2023.
Donna Spencer, The Canadian Press