Carlsson led a 4-on-3 rush through the neutral zone, got the puck back and then fed Kreider, who turned 35 on Thursday, for a one-timer from the right circle and a 2-0 lead at 13:43.
"Pretty much the story for most of the year was we didn't defend well enough," Edmonton coach Kris Knoblauch said. "Usually, you win or lose on your defensive play and it wasn't good enough."
Dostal couldn't control a rebound and Josh Samanski passed the puck through the crease to Murphy, who flipped it into the top of the net with a backhand to cut it to 2-1 at 15:14.
Anaheim, which came into the game 7-for-14 on the power play in the series, scored on its first man-advantage when Gauthier's one-timer from the right circle went off the stick blade of Oilers defenseman Darnell Nurse and fluttered over Ingram's right shoulder for a 3-1 lead at 16:50.
"Our power play scored a very timely goal for us," Ducks coach Joel Quenneville said. "The special teams were special in the series and it made a big impact."
Dostal, who was removed in the first period of Game 5 after giving up three goals on nine shots in the 4-1 loss, stopped Zach Hyman on a partial breakaway at 4:36 of the second period, and Hyman put the puck in the net at 18:28, but it was quickly determined he used a kicking motion.
Terry then finished off a 2-on-1 rush with Carlsson to extend the lead to 4-1 with 47 seconds left in the second period.
“There’s been a lot of talk about their speed and skill, but there’s a lot of size," Knoblauch said of the Ducks. "They forecheck hard and win battles. … They have a lot of ingredients to be a good team.”