His first career goal stood up as the game-winner in Calgary's 4-2 playoff win over the Vancouver Canucks on Sunday.
Calgary took a 2-1 lead in the Western Conference quarter-final series with Game 4 back at Scotiabank Saddledome on Tuesday.
The best-of-seven series returns to Vancouver for Game 5 on Thursday.
Bennett scrambled to the net to slip a rebound past Vancouver goaltender Eddie Lack and give Calgary a 3-1 lead at 2:14 of the third period.
"It's a moment I've thought about for a very long time," the 18-year-old said. "I've been told to drive the net so that's what I'm going to do."
According to the NHL, he's the youngest Flame to ever score a game-winning goal in the post-season.
Flames defenceman T.J. Brodie contributed a goal and an assist, with 20-year-old centre Sean Monahan collecting his first-career playoff goal and Brandon Bollig scoring for the first time since Feb. 2.
Goaltender Jonas Hiller made 23 saves for the Flames, who were hosts of an NHL playoff game for the first time since April 27, 2009.
The Saddledome began chanting "Go Flames Go" several minutes before the opening faceoff, which Flames head coach Bob Hartley said the team could hear in their dressing room.
Shawn Matthias and Jannick Hansen countered for the Canucks, with Lack stopping 24 shots in the loss.
Bennett recorded an assist in his NHL debut in Calgary's regular-season finale. The fourth overall pick in last year's NHL draft was a speedy, scrappy presence for the Flames in their first two games of the series in Vancouver.
With a ferocious forecheck and screens in front of Lack, he and linemate Joe Colborne created time and space for Brodie to tee up a slapshot from inside the blue-line and give Calgary a 2-1 lead after one period Sunday.
Colborne also had a hand in Bennett's goal with a sharp-angled shot that Lack couldn't corral. It was Bennett's first game at the Saddledome since a pre-season game Oct. 2.
"Sammy, you should have seen the smile on this kid's face on the bench after his first goal," Hartley said. "He makes things happen out there. His speed, his determination, he's a special young man."
Calgary opened the best-of-seven series with a 2-1 win, but fell 4-1 in Game 2 at Rogers Arena. That second game in Vancouver ended with a line brawl and 132 minutes in penalties assessed.
The animosity re-surfaced in a scoreless second period Sunday with jawing, face-washing and shoving after whistles that continued into the third.
Calgary forward Johnny Gaudreau skated to the bench in pain after he was chopped across the arms by Vancouver defenceman Dan Hamhuis, but continued to play and assisted on Monahan's goal.
Flames defenceman Kris Russell and Canucks forward Alex Burrows fought with a minute 25 seconds remaining, followed shortly after by a scrap between Calgary's Michael Ferland and Vancouver's Kevin Bieksa.
With Vancouver's Yannick Weber serving a goaltender interference penalty and Hamhuis joining him in the box for an illegal check to Bennett's head, Monahan scored his first NHL playoff goal on a two-man advantage at 14:36 of the third.
Hansen reduced Calgary's lead at 17:41 of the third. The Flames held Canucks stars Henrik and Daniel Sedin to a combined two shots in the game.
Vancouver carried a 30-19 edge in hits in Game 2. Led by Ferland with eight, it was the Flames doing the banging Sunday by a 33-18 margin.
"They had a good forecheck. That's the bottom line," Canucks head coach Willie Desjardins said. "I thought they played physical all night. They did a good job on us and we weren't good enough.
"We were outshooting them going into the third. We just took ourselves out with penalties in the third. They're not under our skin."
Notes — Mason Raymond, who was a healthy scratch the first two games of the series in Vancouver, assisted on Bollig's goal . . . Calgary also took F Markus Granlund and D Corey Potter out of the lineup and inserted D Tyler Wotherspoon . . . According to the NHL, Bennett at 18 years, 303 days is also the second-youngest Flame to score a playoff goal. Former captain Jarome Iginla is the youngest at 18 years 297 days.