Defenseman Sami Salo followed a shot from team mate Steve Bernier for the go-ahead goal with just 1:13 remaining before Ryan Johnson added an empty-netter as the Canucks took a 1-0 lead in the best-of-seven series.
"Our emphasis has been to have our defenders jumping in (around the net), and tonight we had a 3-1 advantage and I stopped in front of the net," Salo told reporters.
"(Chicago) made some good plays and found a way to come back. We can't be happy about the third period."
Vancouver, who swept past the St. Louis Blues in the first round, improved to 5-0 in the postseason but not before some nervous moments down the stretch.
Trailing 3-0 heading into the third period, Chicago's Patrick Kane scored twice in a span of 10 minutes and Dave Bolland added his first goal of the playoffs to erase the deficit at 14:31 in the third.
"It's tough to lose like that, especially with a minute left," Kane said. "At the same time we put together a good third period so we can build on that. We have to use that to go into the next game."
Luongo finished with 28 saves after cruising through the first two periods as the Canucks built an advantage on scores from Pavol Demitra, Henrik Sedin and Ryan Kesler.
A mass brawl and 80 minutes of penalties marred the last contest between the two teams but Thursday's game contained no such physicality. Game Two is on Saturday in Vancouver.
