Luongo, fourth among active goalies with 42 career shutouts, made his best saves early and late, including a short-handed breakaway stop on Garth Murray in the opening minutes after Bieksa's point shot was blocked.
Luongo secured his third shutout in five games and NHL-leading fourth overall with a dramatic glove save on Ed Jovanovki's blast with 25.2 seconds left and the Phoenix net empty for an extra attacker. In between, the star goalie got a lot of help from a stingy defense that kept the Coyotes to the outside most of the night.
"I felt pretty good, but guys are doing a great hob in front of me, too," said Luongo, who also made 28 saves to blank Nashville on Tuesday and Los Angeles last Friday. "When we help each other out like that on the ice, we get good results."
They could have been better if not for Ilya Bryzgalov, who made 31 saves, but couldn't end the Coyotes' seven-game pattern of alternating losses and wins.
"Bryz matched (Luongo's) effort and was our best player tonight for sure," Jovanovski said. "The first couple of periods, (Luongo) didn't really have to work too hard, but in the third, especially toward the end, he made some real good saves."
Bryzgalov kept Phoenix in the game with a handful of brilliant saves - the best a sliding glove stop to take away an empty net from Mason Raymond midway through the second period. Bryzgalov also stopped Raymond's shot on a 3-on-1 with three minutes left.
But Bryzgalov didn't have a chance on the Canucks' only goal. After Daniel Sedin hit the post twice in the first three minutes, Bieksa joined the rush to create a 3-on-2 that became a 2-on-1 after Ryan Kesler drew a defender and passed to Alex Burrows. Bieksa buried Burrow's cross-ice pass with a 20-foot wrist shot.
"I didn't really have to do a whole lot, just jump up in the play," Bieksa said. "Kes and Burr made a great play and I had an empty net and I'll take those."
At the other end, Luongo got a break when Peter Meuller's shot on the power play deflected off the post with 5 minutes left in the first period, and the goalie forced Stephen Reinprecht to shoot wide alone in tight with 30 seconds left.
Luongo wasn't tested for 13:45 of the second as the Coyotes failed to register a shot until they were on a power play, but was forced to make nine saves over the final six minutes of the second period. He also stopped Olli Jokinen in tight on power-play rebounds early in the third, and Viktor Tikhonov on a short-handed 2-on-1 with seven minutes left as the Canucks won for the fourth time in five games.
"We had some good opportunities to put the game away but met a solid goaltender, just like they met a solid goaltender," Canucks coach Alain Vigneault said.
Luongo hasn't given up a goal in just over seven periods, but is still more than a full game away from the franchise record he set with three straight shutouts -- 210 minutes, 34 seconds in total -- through early December of last season.
"It's a combination of things," Luongo said. "I feel good. The guys are playing well in front of me. We're getting some good bounces our way."
The Coyotes finished 0-for-3 on the power play, but were undone just as much by taking three of their seven penalties during the third period.
"It's a tight close-checking game. You need a couple of your big boys up front to score and we didn't get that," coach Wayne Gretzky said. "You're not going to be successful against a good team if your top echelon guys aren't there.
- Phoenix rookie Kyle Turris, the 19-year-old third overall pick in the 2007 draft, was a healthy scratch for a second straight game despite saying before the game he expected up to 100 friends and family for what would have been his first NHL game in his hometown.
- Canucks D Lawrence Nycholat, who has only played three of 14 games this season, was sent to Manitoba of the AHL on a conditioning assignment.
- A reporter from Denmark was on hand to chronicle what would have been the first NHL game between two Danish players, but had to settle for Coyotes rookie Mikkel Boedker because Canucks rookie Jannik Hansen has a groin injury.