Nick Holden and Max Pacioretty scored, and Malcolm Subban made 25 saves for the Golden Knights (9-12-1), who have lost two of the past three and four of the past six.
"There's too many games this year where that's happened," Vegas forward Reilly Smith said. "We're probably going to have to dissect this one."
The Flames scored five first-period goals at home for the first time since March 11, 1993, against the Detroit Red Wings.
Tkachuk scored on the power play on Calgary's first shot of the game for a 1-0 lead at 2:36, and Gaudreau finished a three-way passing play with Elias Lindholm and Monahan to score his first goal in eight games and make it 2-0 at 6:49.
"The past few games I haven't been finding the net. Been getting good looks -- hitting posts, crossbars, getting some good chances," Gaudreau said. "It was nice to capitalize tonight and get rewarded in that department."
Monahan extended the lead to 3-0 when he one-timed a pass from Gaudreau at 10:59, and Brodie scored on a point shot through a screen at 13:52 to make it 4-0.
Tkachuk hit the post on a power play, and Monahan scored on the follow-up to push the lead to 5-0 at 16:57. Monahan has six points (four goals, two assists) in his past four games.
"It's fun, obviously, when you're putting the puck in the net and you're winning like that," Monahan said. "That's the best part of hockey."
Tkachuk scored 24 seconds into the second period to make it 6-0, and a point shot deflected off Bennett on the power play at 4:22 to extend it to 7-0.
