Playoff success usually requires a little discomfort, and the Ducks got a good taste of both in their opener.
Getzlaf, Kyle Palmieri and Mathieu Perreault scored in a dominant first period for the top-seeded Ducks, who began their playoff run on a dead sprint. Anaheim led 4-0 midway through the second period before Dallas got rolling in its first playoff game since 2008.
Captain Jamie Benn and Colton Sceviour had power-play goals, and Tyler Seguin scored with 6:07 left to trim the Ducks' lead to one. Anaheim hung on with a handful of big saves from Andersen, a 24-year-old Danish rookie.
"We knew they were going to push," Palmieri said. "No team is going to go away, especially in the playoffs. We weathered the storm, and it'll help us going forward."
Game 2 of the best-of-7 series will be Friday.
Anaheim is the Western Conference's No. 1 seed for the first time after the best regular season in franchise history, setting new marks for victories (54), points (116) and goals (263) while winning its second successive Pacific Division title.
The Ducks won their opener for the second successive year, but they lost in seven games to seventh-seeded Detroit last spring. They didn't even get 60 minutes into their postseason return without drama, nearly blowing a four-goal lead while losing two of their top-line forwards to injury.
"I'm sure we didn't put the fear of God in them tonight, and they probably gained some confidence," coach Bruce Boudreau said. "We didn't play that good. We gave the puck away too many times tonight, but we'll go back to the drawing board."
Matt Beleskey had a goal and an assist before incurring a lower-body injury in the third period. Getzlaf then got hit in the face with the puck with 16 seconds left, sending him to the dressing room early.
Beleskey has struggled with a similar injury in recent weeks, and Boudreau wasn't sure of its new severity. Boudreau doesn't think Getzlaf has a broken bone in his face, but will know more Thursday when the Ducks reconvene to figure out what to fix from Game 1.
Benn and Sceviour scored in their postseason NHL debuts, but the Stars couldn't escape their early hole despite an impressive game from their high-scoring top line of Benn, Seguin and Valeri Nichushkin, which accounted for 14 shots.
"The way we finished was how we want to play the full game," said Seguin, who infamously scored only one goal in 22 playoff games for Boston last season. "I definitely liked our no-quit attitude out there and performance."
Kari Lehtonen stopped 31 shots for the wild-card Stars, who ended their five-year playoff drought thanks to new coach Lindy Ruff and seven Stanley Cup winners on their roster.
"I thought at times we had them on their heels, and we gave them a good push," Ruff said.
Andersen, who went 20-5 in his first NHL season, got the start over veteran Jonas Hiller, who has fallen out of favor with coach Bruce Boudreau after a handful of poor starts.
After a raucous pregame reception from their orange towel-waving fans, the Ducks wasted no time. Nick Bonino lifted an exceptional pass over diving defenseman Aaron Rome to Palmieri for a backhand goal only 1:53 in.
Getzlaf converted a rebound of Beleskey's shot off Lehtonen's mask, and Perreault put Anaheim up 3-0 with a power-play goal on exceptional passes from Patrick Maroon and Getzlaf.
Beleskey got credit for the Ducks' second power-play goal when Francois Beauchemin's long shot deflected off his leg.
But Dallas got a 5-on-3 advantage for 56 seconds late in the period, and both Benn and Sceviour capitalized.
Stephane Robidas faced his former teammates for the first time since Dallas traded the veteran defenseman to Anaheim last month. ... Anaheim's long-struggling power play hadn't scored multiple goals in a game since Jan. 15, when the Ducks got six against Vancouver. ... LW Ray Whitney returned to the Stars' lineup after missing the last six games with a lower-body injury. ... Nichushkin, who turned 19 last month, made his NHL playoff debut two months after playing in his first Olympics for Russia.