Zack Kassian scored a second-period goal and the Canucks won their second in a row, defeating the struggling Oilers 2-1.
The Canucks were without leading scoring Sedin, who missed his first game in close to a decade with an injury, and John Tortorella, who started his 15-day suspension for an altercation during a game against the Calgary Flames on Saturday.
"I think we all have to step up," Luongo said. "It's not just one person, that's what good teams do. When there's guys out of the lineup other guys have to step up and those coming into the lineup have to play well.
"Good teams find a way to do that and (Tuesday) we played a great game."
Canucks assistant coach Mike Sullivan said his team's good start proved essential when the Oilers started to battle back in the third.
"I thought we played hard, I thought we played smart, the first two periods I thought we played real well," he said. "We were playing with fire there in the second, they have a lot of skill and their power play was really good. I thought once we killed that off to get out of the second period, the key for us was to make sure we didn't give them another opportunity."
Jordan Eberle scored for the Oilers, who have lost five in a row and 10 of their past 12.
It was also Edmonton's fourth losing streak that has gone five games or more this season.
"We could have had two or three goals on the power play, but Luongo made some really good saves," Eberle said. "I thought we played a pretty good game, we just couldn't find a way to score. I think for sure the saves he made on our power plays made the difference."
Oilers captain Andrew Ference said some progress was made, but it may have been a case of too little, too late.
"We showed some great fight at the end and good pressure and some good chances," he said. "The penalty kill was excellent tonight. It was good, but there was still that extra little bit that everybody feels was left on the table a little bit at certain points in the game."
Vancouver got on the board at 5:14 of the first as Oilers goalie Ben Scrivens allowed a big rebound on a long shot from Dale Weise. Lain was there to swat at the rebound that glanced off Scrivens' arm and in.
It was Lain's first career NHL goal in just his second game. He played only 2 seconds in Vancouver's fight-filled win over Calgary.
"You always dream of playing in the NHL, but you also dream of scoring that first goal," Lain said. "When you get it, it's a pretty special moment. I just drove to the net and the puck just popped out to me."
Vancouver had nine first-period shots to Edmonton's six on Luongo.
Shortly after killing off a penalty where Luongo stood tall on several good Oilers chances, the Canucks made it 2-0 at 7:59 of the second period as Ryan Kesler spotted Kassian streaking toward the net and sent a pass to set up a floater of a shot that beat Scrivens up high. It was Kassian's 10th of the season.
Luongo did his part to keep the two-goal lead intact with five minutes to play in the second as he came across to make a huge blocker save in tight on Eberle with the Oilers on the power play.
Eberle, who also hit a post early in the third period, scored with five minutes remaining as Sam Gagner crashed the crease and a scramble ensued before the puck came loose. Eberle was able to send it through to make it 2-1 and spoil Luongo's shutout bid.
Edmonton had its chances late in the game with Scrivens on the bench, but couldn't get another goal past Luongo. Scrivens finished with 25 saves.
The Canucks return home to start a four-game homestand against Nashville on Thursday. The Oilers next game is on Friday, when they play host to the Phoenix Coyotes.
It was the third of five games between the Pacific Division rivals. Vancouver won both of the previous encounters. The Canucks entered the game having won eight of the previous 11 games between the two squads. ... A pair of players acquired during Edmonton's four-game road trip made their Oilers debut as the fans got their first looks at forward Matt Hendricks (traded from Nashville) and Scrivens (trade with Los Angeles). Scrivens, from the Edmonton satellite community of Spruce Grove, Alberta, was playing his first game in Rexall Place. ... The Oilers were missing forwards Ales Hemsky (foot) and Nail Yakupov (head) and defenseman Philip Larsen (illness). Defenseman Corey Potter returned from missing the past 11 games with a groin injury. ... Also out for the Canucks were Mike Santorelli (shoulder), Ryan Stanton (ankle), Andrew Alberts (concussion) and Jordan Schroeder (ankle).