Rookie Frederik Andersen made 34 saves in his second postseason start, and Andrew Cogliano scored a short-handed goal in the third period as the Ducks moved halfway to their first series victory since 2009. Anaheim has won just one postseason round since its only Stanley Cup title in 2007.
Kari Lehtonen stopped 16 shots, while Alex Chiasson and Ryan Garbutt scored for the wild-card Stars, who took two one-goal losses to open their first playoff series since 2008.
Game 3 is Monday in Dallas.
Getzlaf was hit in the face by Tyler Seguin's shot in the final minute of Game 1, leaving him with bruises and a ragged cut on the left side of his face. His wife then gave birth to their third child early Friday morning, a daughter named Willa.
None of it could stop Anaheim's captain from getting back in the lineup and making enormous plays to keep the Ducks on track. He wore a clear facemask around his jaw and mouth in a prudent concession by a player who doesn't like even wearing a visor.
After a raucous pregame ovation from an Orange County crowd that recognized his toughness, Getzlaf then scored a first-period goal and set up Cogliano's short-handed tally in the third period.
Perry hadn't scored a playoff goal in 10 games since April 2011, getting blanked during the Ducks' seven-game loss to Detroit in the first round last spring. But the Canadian Olympic gold medalist knows how to fill a net: He was the NHL's second-leading goal-scorer this season, trailing only Alex Ovechkin.
Half of Dallas' skaters made playoff debuts in the series opener, but the Stars came out for Game 2 with more confidence and poise from the opening faceoff, and Chiasson put Dallas ahead early on a power play, one-timing a pass from captain Jamie Benn for his first career playoff goal.
Both teams had an added physical edge in the rematch. Trevor Daley jumped on top of Perry and pummeled him with both hands in the Stars' crease during the first period in response to a perceived slight.
Anaheim struggled to match the Stars' pace early, but after another fruitless Ducks power play, Getzlaf evened it by himself. He took the puck away from Erik Cole and skated in on Lehtonen, scoring high for his second goal of the series.
Perry put the Ducks ahead late in the first period after intercepting a pass between Seguin and Benn before rocketing a slap shot past Lehtonen from close range.
Anaheim killed a penalty to end the third period and then extended its lead during another kill early in the third. Cogliano, the Ducks' dominant forechecker and penalty-killer, got away with breaking Sergei Gonchar's stick in the Dallas end before Getzlaf controlled the puck and fed Cogliano for the score.
Garbutt kept the Stars close with a goal in front of Andersen on a setup from Shawn Horcoff midway through the third. Dallas tilted the ice decidedly in its favor in the final minutes, but Anaheim killed a penalty on Getzlaf with 3 minutes to play before surviving a last-minute scramble. Nick Bonino blocked the Stars' final shot.
NOTES: Dallas D Brenden Dillon missed his third straight game with a lower-body injury, and the Stars scratched veteran D Aaron Rome in favor of rookie Kevin Connauton, who made his playoff debut. ... The Ducks played without top-line forward Matt Beleskey, who aggravated a persistent lower-body injury late in Game 1. Devante Smith-Pelly replaced Beleskey in the Anaheim lineup, making his NHL playoff debut.