TJ Brodie had Calgary's other goal, while goalie David Rittich finished with 19 saves.
"I'm more mad because we let (Rittich) out to dry," Tkachuk said. "He doesn't deserve that. We've got to start bearing down and playing for him."
Ryan Carpenter, Reilly Smith, Alex Tuch, Luca Sbisa and Erik Haula tallied a goal and an assist each for the Golden Knights, who sit atop the Pacific Division standings with a 40-16-4 record.
"We didn't have as much push back as we normally do," said Calgary coach Glen Gulutzan. "We didn't create as much offence. In a game like this on the road, you've got to have a little bit more."
William Karlsson and Cody Eakin also scored for the Knights, while netminder Marc-Andre Fleury stopped 28 of 31 shots he faced.
After Carpenter scored an early goal for Vegas, Brodie drove hard to the net to redirect Travis Hamonic's shot past Fleury at 16:15 of the first period.
Karlsson, who was denied on a breakaway opportunity earlier in the period, redirected a pass from Smith past Rittich for a powerplay goal with 30.7 seconds remaining before the first intermission
Just 20 seconds into the middle frame, Hamilton snapped a shot from a sharp angle past a stunned Fleury to pull the Flames into a 2-2 tie.
Smith replied with his 20th goal of the season 58 seconds later to put Vegas back up by a goal.
The Flames evened the score again at 11:07 of the second when Hamilton banked a pass of the skate of Eakin that hit Tkachuk on its way into the net behind Fleury.
Tuch then snapped a shot to the top corner, short side past Rittich 2:51 later to put the home side back up 4-3.
The Flames appeared to tie things up once again early in the third when a slap shot by Giordano bounced off the end boards out front to Monahan, who tapped it past Fleury. The goal was subsequently disallowed after the Golden Knights successfully challenged that the play was offside.
"4-3 in the third, we're in a decent spot and then we get one disallowed and it seemed like they grabbed some momentum," said Flames captain Mark Giordano. "We obviously have to deal with things better than that."
Sbisa put the Knights up by a pair at 3:17 of the final frame when he blasted a point shot through traffic past Rittich for his 100th career NHL point.
Sbisa then fired another shot from the point that deflected off of Haula and in before Eakin scored his seventh goal of the season to round out the scoring.
