Gibson earned his fourth shutout of the season and 16th of his career. He is 12-3-1 in his last 16 starts.
Francois Beauchemin had a goal and an assist for Anaheim, and Andrew Cogliano, Ondrej Kase, Hamphus Lindholm also scored for the Ducks, who've won four straight and are tied with Colorado for sixth in the Western Conference, one point ahead of the Los Angeles Kings.
The Flames have dropped four straight and are seven points out of the final wild card.
Gibson made his best stops in the third period. A couple minutes apart, he stuck out a pad to deny Dougie Hamilton's one-timer, then turned aside Johnny Gaudreau on a breakaway as the Flames fell to 15-18-4 at the Scotiabank Saddledome and were booed off the ice after.
One of Calgary's issues has been the power play, which went 0 for 2 to fall to 1 for 35 in the last 12 games. And it was while the Flames were on the man advantage that Anaheim took the lead.
Less than a minute after Hamilton put a shot off the crossbar, Hamilton and Mark Giordano got tangled up in their own corner, allowing the puck to squirt free. Cogliano corralled it and made a nice move on Smith for a short-handed goal.
Anaheim made it 2-0 at 8:58 of the second when Kase broke in off the wing on a 1-on-1, spun around and put a backhand shot through Smith's pads. The Ducks went ahead 3-0 with 1:05 left in the period on Lindholm's slap shot from the blue line.
Calgary trailed 3-0 despite holding a 23-11 edge in shots on goal. Smith has struggled since returning from a lower-body injury two weeks ago that sidelined him for a month.
Calgary forward Matt Stajan appeared in his 1,000th career game, including 555 with the Flames. ... Anaheim's Jason Chimera, who shook Stajan's hand at center ice during warm-up, played in his 1,100th career game. ... Flames scratches included TJ Brodie (upper body) and Matthew Tkachuk (upper body)... Josh Manson (upper body) missed his first game of the season for the Ducks.
Ducks: Play at Winnipeg on Friday night.
Flames: Play at San Jose on Saturday.
More AP hockey: https://apnews.com/tag/NHLhockey