"I really liked our game tonight," Giordano said. "I liked how we stuck with it. We were down one the whole game, but we didn't take any unnecessary risks.
"That's twice now we're we've been able to get a point in a 6-on-5 (situation), and tonight we got the extra point. Those are going to be huge at the end of the year."
David Rittich stopped 28 shots to record his third win of the young campaign.
Meanwhile, Gaudreau extended his grip on the team points lead with 16 (6G, 10A) after potting the winning marker.
"We had kind of a 3-on-2 coming towards us, and especially with me being on defence, you don't want that too much," he laughed. "(Giordano) did a great job breaking that play up, came back and found a way to beat both their guys up the ice. ... It was a nice play overall."
The Flames, who entered the night with a league-leading 19 third-period goals, applied all kinds of pressure in the final frame, and finally broke through and got one with 55.3 seconds to play to send the game to overtime.
Like he did on Saturday against the Washington Capitals, Tkachuk played the hero in the waning moments of regulation, tipping an Elias Lindholm point shot past Carter Hutton to score his fifth of the year.
"I liked the way we played," said head coach Bill Peters. "I thought we stuck with it. We didn't become high-risk in order to generate our chances. I thought we could have got on the board earlier than we did, but we stayed with it and got a big goal 6-on-5.
"I liked the composure on the bench. We had a little adversity there in the second, and then we moved on. I didn't think we gave up as much as the game went along. I thought we were dangerous, at times, and we'll continue to work on that, too."
The Flames carried the play for much of the opening 20, but a sloppy, neutral-zone turnover with three-and-a-half minutes to play proved costly, as the sharp-shooting Jack Eichel did what he does best and drew first blood for the homeside.
With the Flames trying to re-group and settle the Sabres' counterattack, Jason Pominville made a great play at the blueline, twisting his way into the middle before dishing off to the Buffalo captain. With speed down the far side, Eichel took the pass in full stride and rifled a shot top shelf to give the Sabres a 1-0 lead.
The Flames, aided in part by a pair of early powerplays, had an 11-4 lead on the shot clock at one point, but went the final eight minutes of the period without testing Buffalo goaltender Carter Hutton.
But that changed in a hurry.
The Flames had a spur in their stride early in the middle frame, charging out of the gates with 10 shots in the opening four-and-a-half minutes, but Hutton - emphatically - stood his ground.
With the goalie at his mercy, Sean Monahan passed off to Lindholm at the far post. The Flames' leading goal-getter promptly released a one-timer, but Hutton somehow slid across and made a gargantuan goal-line stop with the blade of his goalstick.
Gaudreau was quick to the scene and thusly deposited the rebound, but a quick whistle nullified the goal and the Sabres remained in front, 1-0.
In all, the Flames outshot the Sabres 38-29.
"It's difficult, at times, when you're getting some chances and not (getting rewarded)," Gaudreau said, "but tonight, we did a great job sticking with it."
