After losing a shutout bid in the dying seconds of Sunday's win over the Colorado Avalanche, Luongo would not be denied against the punchless Oilers and is now just one back of Patrick Roy for 14th on the all-time list.
Daniel Sedin, Zack Kassian, Chris Higgins and Dale Weise scored for Vancouver (19-10-5), which improved to 4-0-0 on its current five-game homestand. Jason Garrison added three assists, while Ryan Kesler chipped in with two of his own.
Devan Dubnyk made 36 saves for Edmonton (11-20-3), which has lost two straight.
The Canucks don't have long to celebrate with the Boston Bruins set to play at Rogers Arena on Saturday night for the first time since their victory in Game 7 of the 2011 Stanley Cup final.
Leading 1-0 after the second period, Vancouver doubled its lead at 2:26 of the third when Kassian deflected a shot from David Booth past Dubnyk for his sixth goal of the season and first point in nine games.
Higgins then stretched the lead to three at 6:07 when he took a feed from Ryan Kesler and beat Dubnyk with a lightning-quick release for his ninth of the campaign. Higgins now has two goals and five assists during his four-game point streak.
Luongo made a big glove stop on Oilers defenceman Justin Schultz midway through the period before Weise had a chance to make it 4-0, only to see his shot hit the post.
Luongo then shot out his left pad on Edmonton forward Ryan Jones to preserve the shutout with under six minutes remaining.
Weise finally found the mark on the power play with 34.8 seconds left on the clock for his third of the season.
After a scoreless first that saw the Canucks carry the play, Vancouver came out strong again in the second and took the lead on a 4-on-3 power play midway through the period.
Implored by Canucks head coach John Tortorella this week to shoot more, Sedin snapped a five-game goalless drought with his 11th of the season when his shot from the point went in off Oilers defenceman Nick Schultz at 8:41.
Higgins had just hit the post behind Dubnyk moments earlier, with Edmonton's Mark Arcobello going off for slashing to give Vancouver the man advantage.
The goal energized the Oilers, who were playing their second game in as many nights, with Luongo robbing David Perron with his glove a few minutes later.
Weise and Kesler then found themselves in alone on Dubnyk on a 2-on-0, but the Oilers goalie stopped Kesler.
Vancouver beat Edmonton 6-2 at Rogers Arena on Oct. 5 and came out firing in the first period on Friday.
The Canucks hemmed the Oilers in their own zone off the opening faceoff and led 6-0 on the shot clock when Edmonton's Ryan Nugent-Hopkins finally directed his team's first effort at Luongo with just under seven minutes gone.
Dubnyk, who was pulled after giving up three goals in Thursday's 4-2 home loss to Boston, had to be sharp a few moments later with big stops on Kassian and Jannik Hansen.
Not to be outdone, Luongo kept out Edmonton's best chance of the period with a sprawling stick save off Ales Hemsky on a 2-on-1.
The Oilers had the only power play of the period when Canucks captain Henrik Sedin was whistled for goaltender interference with under four minutes to go, but Vancouver's No. 1-ranked penalty killing unit had the best chance when Dubnyk just got a piece of Kesler's effort.
Notes: Friday's matchup was Kassian's first against the Oilers since his eight-game suspension for hitting Sam Gagner in the head with his stick during the pre-season. The Edmonton forward missed 13 games with a broken jaw. ... Oilers forward Boyd Gordon returned to the lineup after missing six games with a shoulder injury. ... Edmonton's four-game road trip continues Sunday against the Anaheim Ducks. ... After Saturday's meeting with the Bruins, the Canucks open a three-game road trip against the Minnesota Wild on Tuesday. ... The third of five meetings between the Oilers and Canucks goes Jan. 21 in Edmonton.