Luongo saw his shutout streak against the Wild at home end at 228 minutes and 26 seconds but held on for the win.
He still has not lost a game in regulation this year and lowered his goals-against average to 1.45, behind only Ottawa's Craig Anderson.
Devin Setoguchi replied for Minnesota (6-6-1), who saw their modest two-game win streak snapped. The Wild have not won in Vancouver since Jan. 31, 2009 (0-9-2).
Darcy Kuemper stopped 28 shots in his NHL debut. Kuemper was called up because Josh Harding was battling the effects of medication he takes in dealing with multiple sclerosis. Kuemper has a 1.79 GAA and 0.938 save percentage playing for the Houston Aeros, the Wild's top AHL affiliate.
Bieksa opened the scoring for Vancouver at the tail end of a power play.
Kassian rushed past a defender along the right boards and centred to Bieksa, who beat Kuemper low with a one-timer at 11:33 of the first.
Luongo made his first big stop about 13 minutes into the game during a Minnesota power play, kicking out his right pad to rob Charlie Coyle's one-timer from the slot.
Mason Raymond and Keith Ballard combined to set up Hansen's third of the year at 10:03 of the second. Raymond began the play by skating through three Minnesota defenders before feeding Ballard along the left boards. Ballard spotted Hansen at the right side of the net and the Danish right winger beat Kuemper glove side, off the crossbar and in.
Raymond extended his point streak to four games.
Setoguchi got the Wild on the board three minutes later on the power play with a highlight-reel finish. Mikael Granlund and Matt Cullen worked to dig the puck out of the corner, allowing Setoguchi to walk out front, drag the puck to his forehand and roof the puck past Luongo.
It was Setoguchi's second goal in three games after going nine games without one to start the season.
That goal came on the third of just four shots in the period by the visitors.
Vancouver came out of the second intermission looking to regain the two-goal cushion. Daniel Sedin had a partial breakaway but was turned aside by Kuemper's quick blocker save, keeping the Wild within one.
Minnesota was stymied on their best chance to tie the game just past the five-minute mark. Zach Parise found himself alone in front. His quick shot was kicked out to Ryan Suter in the slot but the defenceman wrung his shot off the iron. Suter has yet to record a goal for the Wild since joining the team via free agency in the off-season.
In the final minute, with Kuemper pulled for the extra attacker, Luongo made a big stop off first Setoguchi and then blocked the rebound. He made 10 stops in the final period.
NOTES: Henrik Sedin entered the game one point shy of Markus Naslund's Vancouver Canucks scoring record and remained stuck at 755. The Canucks' captain also extended his goal-less drought to 12 games to begin the season.