Patrick Eaves and Chris Wagner also scored for the Ducks, who are first in the Pacific Division with 101 points.
The two teams would meet in the opening round of the playoffs should the standings hold.
"I think there's lots of things to build on if this is our opponent come playoff time," Calgary coach Glen Gulutzan said. "I wasn't unhappy with the game. I like the way we stuck together in the third. We didn't get the win, but there are positive things from this game we'll take."
The third period featured a combined 106 minutes in penalties including fighting majors for Giordano and Josh Manson, Matt Barkowski and Korbinian Holzer, and misconducts to Backlund, Deryk Engelland, Micheal Ferland and Ryan Kesler.
"We stick together as a team," Backlund said. "We're a tight group. If they go after us, we're going to respond, of course.
"I thought we did a good job of that."
The physicality ramped up after Giordano collided with Ducks defenceman Cam Fowler inside the Flames end early in the period. Fowler left the game because of a lower-body injury and did not return.
"You don't like to see guys get hurt," Giordano said. "There is no intent to hurt him. I'm just trying to come across in a 2-1 game to try and stop him from getting to our net. I make a hit. The result . . . I don't know if our legs collided or not. I think they did. I hope it's nothing too serious."
Wagner put the Ducks up 3-1 at 6:43. He took a Logan Shaw pass from below the goal line and shot by Elliott's glove with the third of three unanswered goals for the Ducks, who added two in the second period by Eaves at 0:48 and Bieksa at 13:02.
Johnny Gaudreau was stopped on a breakaway, Sean Monahan denied at the edge of the crease and Michael Frolik struck iron before Backlund put the Flames up 1-0 when slid home a rebound from Mark Giordano's point shot with 4:41 remaining in the first period.
"Especially in the first, I thought we really came out with a purpose," Giordano said. "For whatever reason, we can't find that second one to get up and they do. I think that was the difference, obviously, tonight."
Chad Johnson started the game but left at 5:19 of the first period after sustaining a lower-body injury.
"Hope Chad's okay," Elliott said. "You never like going in and seeing guys hurt. It was just a tough game. You think you get a night off and then you've got to jump back in there."
NOTES:The game featured a combined 67 hits. The Flames are winless in 25 games (0-20-5) at Anaheim dating back to Jan. 19, 2004. For Anaheim, it's the longest home winning streak against one team in NHL history. Lance Bouma finished with a game-high six hits. Michael Stone had five. Forwards Curtis Lazar and Freddie Hamilton and defencemen Dennis Wideman and Rasmus Andersson were scratched for the game.
UP NEXT:The Flames continue with the second stop of their three-game road trip at the Los Angeles Kings on Thursday (8:30 p.m. MT; SN360, SN960).
(With files from Torie Peterson)
