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."
