Michael Bunting scored, and Alex Nedeljkovic made 29 saves for the Penguins (20-22-8), who are 3-6-3 in their past 12 games.
Pittsburgh was coming off a 5-1 win at the Los Angeles Kings on Monday.
"I just didn't think we had the same intentions that we did in the game prior," Pittsburgh coach Mike Sullivan said. "I just didn't think we played with the same conviction."
The Ducks gave up the first seven shots on goal before recording their first at 7:58 of the first period.
"We looked a little bit overwhelmed the first five minutes," Ducks coach Greg Cronin said. "They came out, they were flying. It's funny, when you're coaching a game and a team is playing at that speed, even from the bench, you're like, 'Whoa, this is going to be a long night.' It's hard to play at that pace and that intensity for 60 minutes."
Nedeljkovic made back-to-back saves on Trouba and Robby Fabbri but slid out of the crease on the second save, allowing McTavish to score into an open net for a 1-0 lead at 9:28.
"I think it was a slow start, even with the chances in the first," Penguins captain Sidney Crosby said.
Killorn pushed it to 2-0 with 59 seconds left in the first period. He beat Penguins defenseman P.O. Joseph and Marcus Pettersson to a loose puck and skated in alone before scoring with a wrist shot from the left circle.
"For whatever reason, the first period wasn't the type of game that we wanted to play," Sullivan said. "I thought we responded in the second period. I thought we had a pretty good second period, but obviously the first 20 wasn't good enough."