Dan Vladar got his second straight start - and fourth of the season - after backstopping the Flames to a hard-fought 2-1 overtime loss to the Leafs in Toronto Friday night.
He was simply superb Sunday, making 27 saves for his first-career shutout.
Youngster Walker Duehr made his debut for the Flames, turning the obligatory rookie solo lap before the tilt.
He became the first South Dakota born player to skate in the NHL.
Andrew Mangiapane - with his team-leading 10th of the season - also scored for the Flames, as did Elias Lindholm, who finished with two points, and Nikita Zadorov.
Sean Monahan had two assists in the outing.
The Flames improved to 8-3-4 and will continue this season-long seven-game road trip Tuesday in Philly against the Flyers.
Furthermore, they improved to 8-1-2 when scoring the first goal of the game and 7-0-1 when taking a lead into the third period of hockey games this season.
The Sens were without a handful of players due to Covid-19 protocols, including leading-scorer Drake Batherson.
Last season, these two teams met nine teams as part of the all-Canadian Division with Tkachuk leading the way for the Flames with 10 points (2G, 8A) in head-to-head play against his brother Brady, who was named the 10th captain in Senators franchise history on Nov. 5.
On Sunday, Tkachuk's physicality, soft hands and incredible hockey IQ was on display all night for the visitors, helping pace them to a win after dropping their last three games.
As for Vladar, he was tested early when Egor Sokolov found himself alone in the slot, but the Calgary netminder kicked out his right pad to deny his offering.
Later he picked up a Lassi Thomson point shot through traffic - with Sokolov parked on his doorstep - and snagged it with his glove.
The Flames had to kill back-to-back penalties past the midway mark of the frame, first a two-minute elbow to Erik Gudbranson and with 14 seconds left in it, Blake Coleman was sent to the box for hooking.
The team's PK - which came into the game ranked 10th in the NHL at 84.1% - got the job done, killing off both.
Oliver Kylington - who scored the lone marker in the loss to the Leafs - made a great play to pinch in and break up an attempted Sens clear and then get the puck to Monahan, who circled in the slot and fired a puck that Mangiapane tipped home at 3:53 past Anton Forsberg.