Starting in place of Petr Mrazek, who is day-to-day with a lower body injury, McElhinney stopped 28 shots as the Hurricanes beat the New York Islanders 5-2 to take a 3-0 lead in their second-round series.
The wild-card Hurricanes -- in the playoffs for the first time in a decade -- took a 3-0 series lead for just the second time since they moved to North Carolina in 1997.
After losing the first two games of its first-round series with Washington, Carolina has won seven of eight and will try for the sweep Friday night.
"The next game's always the toughest,'' coach Rod Brind'Amour said. "They're not going to go away. We know that. These games have all been tight -- one-goal games, essentially, and it's going to be like that on Friday.''
At 35 years and 343 days old, McElhinney became the oldest goalie in NHL history to make his first playoff start.
After McElhinney made two bang-bang saves in the second period while doing a split, the crowd chanted his first name.
"It's one of those timely saves that you need to come up with at certain points of the game,'' McElhinney said, "and tonight, it was there for me.''
Mrazek had started all nine postseason games for the Hurricanes, but he left the last one early with an injury that, as is usually the case in the NHL, has not been publicly disclosed. It was the first time all season that the Hurricanes made a midgame goalie switch.
Brind'Amour calls Mrazek's injury "a nagging thing," adding that "I don't know how long it's going to go, but it shouldn't be too long."
Less than 12 months ago, nobody saw a Mrazek-McElhinney combination coming, much less figured the pair would backstop Carolina to the verge of the Eastern Conference final.
When Darling was injured in the preseason finale, Carolina found McElhinney on the waiver wire and the journeyman fit so well with the Hurricanes that they placed the largely ineffective Darling on waivers and sent him to their AHL affiliate in Charlotte.
Carolina allowed 2.7 goals per game during the regular season. Mrazek stopped 91.4 percent of the shots he faced; McElhinney's save percentage was .912. Both of their save percentages are better than any Hurricanes goalie since 2014 with more than 30 appearances.
It's also worth noting that the last time the Hurricanes made a goalie switch during the playoffs, it worked out pretty well for them.
Carolina began the 2006 postseason with Martin Gerber in net, but while dealing with health issues, he gave up nine goals during the first 75 minutes of the Hurricanes' first-round series with Montreal. Coach Peter Laviolette turned to Ward, who led the team captained by Brind'Amour to the Stanley Cup.
The Associated Press contributed to this report.