Rittich made 26 saves in the tilt, but two third-period goals by Andrei Svechnikov erased a 1-0 Flames lead and proved the difference.
It marked the second time Elias Lindholm, Derek Ryan, Noah Hanifin and head coach Bill Peters had returned to North Carolina.
The last time - back on Feb. 3 - the Flames skated to a 4-3 victory, part of a 2-0 season sweep of the 'Canes.
The first good chance of the night Tuesday went to one of the Carolina ex-pats, Hanifin ringing a shot off the post while the teams skated 4-on-4, Mark Giordano in the box on a roughing call he took midway through the Flames first powerplay of the night.
Petr Mrazek benefited from a perfect combination of right-place-at-the-right-time and quick pads to deny Sean Monahan on a one-timer from the doorstep just past the midway point of the period.
In that game on Feb. 3, Lindholm scored.
Fittingly, the man who has two goals and three points during his current three-game point streak and came into the tilt as the hottest Flame, opened the scoring this time around.
Following a faceoff in the Carolina zone, Johnny Gaudreau skated into the corner with former Flames Dougie Hamilton hot on his heels and all over him with his stick but instead of picking up the puck and skating behind the net where Hamilton looked to cut him off, he spun back up the boards.
Lindholm drove the net and then popped back up to the mid-slot wide open and one-timed the perfect feed.
It was his 99th career tally, with Travis Hamonic picking up the other helper.
Less than two minutes later, it appeared that Backlund had made it a 2-0 game. After a Rasmus Andersson shot was saved, Michael Frolik picked up the puck and with two 'Canes on him, feed a no-look backhand pass into the slot that Backlund snapped home five-hole.
However, Carolina challenged and Tkachuk was ruled offside, not clearing the zone before the Flames came back in.
The Hurricanes came out hard in the second period, Brett Pesce getting the first good chance just over a minute into the frame, but Rittich coming up big to stymy him in tight.
It was one of a bevy of 10-bell saves he made on the night.
Later, Mrazek flashed his glove to rob Andrew Mangiapane after a tic-tac-toe passing play on the rush between him and Ryan and Andersson, but the 'Canes were whistled for a penalty.
The ensuing powerplay did everything but score, creating a handful of deadly chances - the best a back-door pass from Gaudreau to Tkachuk that the latter wasn't able to get enough stick on. In total, they got five high-quality chances on the advantage.
Johnny Hockey later set up Tkachuk again, corraling a puck on his backhand as he spun near the blueline, putting it to No. 19 who wasn't able to get past Mrazek.
Carolina came out fast and hard again to start the third, Andrei Svechnikov eventually scoring a rather unorthodox goal at the 9:13 mark to break the shutout bid by Rittich, scooping the puck up on his backhand behind the net and wrapping it around the net in the so-called lacrosse style, knocking it off the goalie's mask and over his right shoulder into the cage.
Just over three minutes later, he scored his second of the night on the powerplay. The goal came on a faceoff after a stoppage of play when Rittich made a save, but was in some pain after being hurt when Erik Haula poked at the puck between the goalie's legs after the whistle. There was no penalty call.
At that point, the shots were 10-0 for the homeside.
The Flames poured it on late in the frame on a powerplay battling for the equalizer, but Mrazek made huge stops on both Gaudreau and Tkachuk in the dying seconds.
THEY SAID IT:
MARK GIORDANO ON TOUGH LOSS
"They pressed really hard all game. I thought there were moments when we were really good, when we were making plays through the middle, and then when we got in trouble, we weren't making clean plays. You gotta give them credit. They are obviously a great team but I think we can be cleaner with our breakouts and execution but at the end of the day, it was a hard-fought game. They get a pretty nice play by the guy from behind the net, I guess, and a powerplay goal, so that was the difference. I thought we had our looks, too, but when you score one, the mistakes get magnified. Tough way to lose."
BILL PETERS ON SVECHNIKOV'S FIRST GOAL
"That's the one we had the puck twice on, right, we had the puck twice on it and turned it over ... Give him credit for the creativity and the execution there but, again, that's one where we have the puck twice. We should be out, we should be gone down to the other end."
"They were skating better than us. They were all over us. We weren't necessarily sitting back but they just took it to us, had all the momentum in the world - that guy scored an awesome goal there to make it 1-1 and then they still have all the momentum in the world and then I take probably an undisciplined penalty that I'd like to have back ... can't have that when they are all over us with momentum. Then it's 2-1 and we just couldn't find an answer fin the last 10 minutes or whatever it was."
Hanifin was hit by a shot during the third period and left the game and did not return ... Alan Quine skated in his 100th career NHL game last night, his second straight tilt since his recent call-up from the Heat.
Here are the forward lines, D pairings and goalie to start Saturday's game (starters in bold):
Johnny Gaudreau - Elias Lindholm - Matthew Tkachuk
Alan Quine - Sean Monahan - Sam Bennett
Milan Lucic - Mikael Backlund - Michael Frolik
Andrew Mangiapane - Derek Ryan - Tobias Rieder
Mark Giordano - TJ Brodie
Noah Hanifin - Travis Hamonic
Oliver Kylington - Rasmus Andersson
The Flames continue this five-game road trip in the Music City on Thursday when they face the Predators (5 p.m., Sportsnet). They finish up with back-to-back games Saturday in Columbus (6 p.m., Sportsnet West) and Sunday in Washington, D.C. (5 p.m., Sportsnet).