The line of Tkachuk, Mikael Backlund and Michael Frolik combined for 11 points (five goals, six assists) for Calgary (42-20-7), which ended a four-game losing streak and moved back into first place in the Pacific Division and Western Conference, one point ahead of the San Jose Sharks.
"We didn't talk about it today at all, but I mean, I would assume if you asked every guy and they gave their honest answer … we don't want to be trailing anybody," Tkachuk said. "We want to win the division. We don't want to finish second, third, fourth, fifth. You never want to be chasing teams, and I think it was a little extra motivation."
[WATCH: All Golden Knights vs. Flames highlights]
Tkachuk had three goals and an assist, Backlund had two goals and an assist, and Frolik had four assists. David Rittich made 25 saves.
"Every time you end a losing streak, it always feels good," Backlund said. "Your shoulders lower a little bit and you get some smiles. I thought right off in the morning and before the game guys were excited, energized. It was a good feeling, I thought, before the game.
"Before in this stretch, it can get a little tough on the group. I thought today we all came in with a smile on our face and were excited to play, and I think that showed on the ice."
Video: VGK@CGY: Backlund wrists one by Subban
Mark Stone, Reilly Smith and Brandon Pirri scored, and Malcolm Subban made 29 saves for Vegas (38-27-5), which is nine points behind the Sharks for second in the Pacific, and eight points ahead of the Arizona Coyotes for third.
"They're a good team for a reason," Golden Knights forward Max Pacioretty said of the Flames. "They were hungry for that win tonight."
Backlund gave Calgary a 4-3 lead at 19:38 of the second period when he redirected Rasmus Andersson's point shot. Vegas coach Gerard Gallant unsuccessfully challenged for goaltender interference.
"I don't think it's a goal," Subban said. "Obviously, they thought otherwise. It's tough. It's the game-winning goal. It's frustrating. They scored six goals, so it's not the reason we lost. But it's definitely a big goal for them."
Tkachuk scored his second of the game, on a pass from Backlund, at 15:43 of the third period to make it 5-3. He completed the hat trick with an empty-net goal at 17:28 for the 6-3 final.
Calgary's first-round pick (No. 6) at the 2016 NHL Draft, Tkachuk has eight points (five goals, three assists) in his past seven games.
"I thought we could've even had a couple more," Tkachuk said. "We weren't in the D-zone too much. All in all, a pretty good night."
Andrew Mangiapane scored 2:40 into the first period to give the Flames a 1-0 lead, and Backlund scored from the high slot to make it 2-0 at 7:37.
Pirri one-timed a pass from Alex Tuch from below the goal line to make it 2-1 at 14:40, but Tkachuk finished a 2-on-1 with Frolik to give Calgary a 3-1 lead at 18:58.
"They gave me a couple tap-in birdies there; a couple open nets," Tkachuk said. "They were awesome tonight to play with."
Smith scored on a backhand 21 seconds into the second to make it 3-2, and Stone scored his 30th of the season 59 seconds later at 1:20 to tie it 3-3.
"The keys to the game were have a good start, and we didn't," Gallant said. "That's basically what cost us the game at the end of the day."
Video: Enterprise Hat Trick: Tkachuk scores three for Flames
They said it
"Our first period wasn't great, but we came back and gave ourselves a chance to win the game. The opportunities were there. We just weren't able to put it into the net." -- Golden Knights forward Max Pacioretty
"It was fun. I think the biggest key was we won the game. We are happy that we could help the team to win and stop the losing streak. We need to keep going and keep building. It was a good night for our line. Hopefully we can keep it going." -- Flames forward Michael Frolik
Need to know
Tkachuk's first NHL hat trick came at the age of 21 years, 89 days. His father, Keith Tkachuk, scored his at 21 years, 209 days. … Flames forward Johnny Gaudreau, who hasn't scored in nine games and has one goal in his past 19, finished with nine shots to tie his NHL career-high (Feb. 11, 2018 against the New York Islanders). … Smith has 10 points (five goals, five assists) in his past nine games; Stone has five points (two goals, three assists) in his past five games.
Golden Knights: At the Dallas Stars on Friday (8 p.m. ET; NHLN, ATTSN-RM, FS-SW, SNO, SNE, SN360, NHL.TV)
Flames: Host the New Jersey Devils on Tuesday (9 p.m. ET; SNW, MSG+, NHL.TV)
Video: Tkachuk's hat trick powers Flames past Golden Knights