The 34-year-old turned aside 35 shots - including all 22 he faced in the third period - to secure his fourth straight victory and sixth in his previous seven starts.
"We got into penalty trouble there in the third and he was there to bail us out, and that's been the storyline this playoffs," he added. "Every time we've needed a big save, he's been there for us."
Khudobin is now 9-1 with a .930 save percentage when facing 30 or more shots in a game this postseason, according to Sportsnet Stats.
His biggest save of Saturday's contest came in the final minutes of the second period, as he reached back to deny Lightning forward Anthony Cirelli during a mad scramble in front of the net. The Stars would add a goal to make it 3-1 just moments later.
Stars defenseman Jamie Oleksiak, who scored the eventual game-winning goal in the second period, said the club has been riding the momentum of Khudobin's hot play all postseason.
"His play's been speaking for itself," Oleksiak said. "It looks like whenever he's out there, he's just having fun. I think we're feeding off that energy. He's been great. I can't say enough about him."
Khudobin stifled the high-powered Vegas Golden Knights in the Western Conference Final, recording a .950 save percentage while allowing just eight goals during the five-game series.
Off the ice, the 5-foot-11 puck-stopper appears to be using his unique sense of humor to keep his teammates loose:
Khudobin will look to pick up his 14th win of the playoffs in Game 2 on Monday after recording just 16 victories during the regular season while serving as the backup to starter Ben Bishop.