Monahan recorded the first hat trick of his NHL career, Gaudreau picked up a goal and two assists to extend his points streak to a career-high nine games, and Michael Frolik scored 1:18 into overtime to provide the margin of victory in Calgary's 5-4 win over the Philadelphia Flyers on Saturday.
The Flames (11-8-0), who were routed 8-2 in Detroit, won for the sixth time in eight games.
''I think the last game in Detroit was a little eye-opening,'' Gaudreau said. ''It's exciting to see us play this way because I don't really think we've seen our best hockey yet.''
Goaltender Mike Smith, who returned from an upper body injury, turned aside 35 of 39 shots to earn his 10th win.
Brian Elliott, who appeared in 49 games for the Flames last season, recorded 27 saves in the loss for the Flyers, who allowed three power-play goals to Monahan in the second period.
''Sometimes it's the penalties that you take that bite you a little bit,'' Elliott said. ''There were little breakdowns and they're a skilled team and made us pay. We took too many penalties in the second period.''
The Flames, who rank last in the NHL on the penalty kill, held the Flyers to just one shot on a power play in the final 2 minutes of regulation.
''We were aggressive,'' Flames coach Glen Gulutzan said. ''You're dealing with the best players in the league and when you give them time and space you're in trouble. Last year we were in the same boat. We were 30th (in the NHL) after 20 games and we ended up (12th) in the league and killed at a high rate.''
The two teams combined for eight goals on 54 shots through the opening 40 minutes.
Manning and Provorov each scored their third goals of the season and Couturier netted his team-high 12th to give the Flyers a 3-1 lead through one period.
Monahan and the Flames' power play took over the game in the second period.
The 23-year-old center redirected a shot by Kris Versteeg to draw the Flames within 3-2 at the 6:07 mark and tied the score less than 4 minutes later by depositing a Gaudreau rebound past his former teammate.
The Flyers regained the lead on Patrick's second goal of the season with 5:58 remaining in the period, but an elbowing penalty to Flyers defenseman Shayne Gostisbehere led to the Flames' third power play of the period. Monahan converted, tying the score again on a shot from the slot with 5:04 remaining for his first career three-goal game.
''I wasn't a good team player on that play,'' Gostisbehere said. ''In the heat of the moment I let my teammates down. I was upset.''
Gaudreau assisted on two of Monahan's three goals and also scored on a first-period breakaway off a long stretch pass from right winger Michael Ferland.
''He's a guy always looking for offense and cutting to the middle,'' Elliott said of Gaudreau. ''He got us on one tonight.''
NOTES: Flyers D Radko Gudas sat out Saturday's game while awaiting a phone hearing with the NHL Department of Player Safety for his slash to the neck of Winnipeg Jets forward Mathieu Perreault. Gudas is expected to have the hearing on Sunday. ... Flames LW Matthew Tkachuk served a one-game suspension for tapping Detroit Red Wings forward Luke Witkowski in the back of the leg on Wednesday night, sparking two fights near the end of an 8-2 loss.
Flames: continue their six-game road trip Monday night in Washington against the Capitals.
Flyers: return to action Tuesday night against the Vancouver Canucks.
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