"It was really fun. It was something I've wanted my entire life," Oettinger said Wednesday. "To have the opportunity in the conference final is really cool. The guys did a really good job in front of me. It was really nice and it was nice to get my first minutes under my belt."
Oettinger saved the five shots he faced in relief of Anton Khudobin, who allowed three goals on 27 shots in the first two periods.
"You put a kid in the net for his first NHL action, and you hope it'll spark some life," Dallas coach Rick Bowness said. "We had a better third period. Anton was the only reason it was 3-0. Without Anton, that's 6-0 after the second period."
Khudobin has started 15 of the 18 games this postseason, including 25 saves in a 1-0 win in Game 1 on Sunday. He is 9-6-0 with a 2.82 goals-against average and .912 save percentage.
A veteran of 218 regular-season NHL games, the 34-year-old had played two Stanley Cup Playoff games, totaling 37:42, prior to this postseason.
"Give him a breather," Bowness said. "He got killed in that second period (19 shots-against)."
Oettinger entered the postseason as the third goalie for Dallas, but the 21-year-old has backed up Khudobin with Ben Bishop unfit to play.
He credited each of them for making him feel he belongs in the NHL.
"They've been unbelievable to me. Obviously two guys that I really look up to," Oettinger said. "They're open books. It's been fun to feel like you're their teammate. They've helped me as much as they can. Just two really, really good guys, two guys who have helped me a lot. They helped me feel comfortable last night. It was really nice. I can't say enough good things about them."
Selected by Dallas in the first round (No. 26) of the 2017 NHL Draft, Oettinger was 15-16-4 with a 2.57 GAA, .917 save percentage and three shutouts in 38 games with Texas of the American Hockey League this season.
Oettinger is the second goalie of the NHL modern era (since 1943-44) to debut in the round leading to the Cup Final. Bob Champoux did so in Game 2 of the 1964 NHL Semifinals when he replaced an injured Terry Sawchuk for the Detroit Red Wings in a 5-4 win. The expansion era began in 1967-68.
Oettinger is the 12th goalie to make his debut in the playoffs. Boston Bruins goalie Dan Vladar became the 11th in Game 3 of the Eastern Conference Second Round against the Tampa Bay Lightning this postseason (a 7-1 loss).
Bishop played 13:43 before being pulled from in his most recent game, allowing four goals on 19 shots to the Colorado Avalanche on Aug. 31 in Game 3 of the second round (a 6-3 loss). He played Aug. 13 against the Calgary Flames in the first round (a 5-4 win) and Aug. 3 against Vegas in the round-robin portion of the Stanley Cup Qualifiers (a 5-3 loss).
Bishop is 1-2-0 with a 5.43 GAA and .844 save percentage this postseason.
NHL.com staff writer Tim Campbell contributed to this report