Mason Raymond scored for Vancouver in regulation, and Luongo made 30 saves in the first 65 minutes.
Despite alternating wins and losses for the past 11 games, Vancouver extended its lead atop the NHL to three points over Philadelphia and five ahead of Detroit in the Western Conference.
Scott Upshall scored in his Blue Jackets debut after being acquired in a trade Monday, then watched nervously as his new teammates killed off the four-minute high-sticking penalty he took with less than five minutes left.
Columbus captain Rick Nash scored to open the shootout, but Raymond tied it in the third round. Antoine Vermette and Alex Burrows traded goals in the fifth round, and Steve Mason made a spectacular left pad save in the sixth before Torres snapped a low shot past Mason's glove to end the game.
Columbus held the NHL s top power play to just two shots and Andrew Murray hit the post on a shorthanded 2-on-1.
Mason made 14 of his 25 saves after the midway point of the third period to help the 12th-place Blue Jackets get at least a point for the 10th time in the last 12 games. Columbus fell five points behind a three-way tie for the final playoff spot in the Western Conference.
Raymond ended an 11-game goal drought with 5:33 left in the first period after some nice work Ryan Kesler, who won a battle with Jan Hejda along the boards and shoveled across to send him in alone in tight.
Raymond, who only had two goals in his previous 26 games and was dropped from the second to the fourth line midway through the last game, made a strong deke to his backhand before lifting the puck over Mason s extended left pad.
Both teams had players making their debuts after being acquired in a trade before the NHL deadline Monday — Upshall and defenseman Sami Lepisto for Columbus, and fourth-line center Maxim Lapierre for the Canucks — and two of them combined on the Blue Jackets' goal 7:11 into the second.
Lapierre lost a battle with Derek Dorsett along the boards and he passed to Samuel Pahlsson, who relayed to Upshall in the right faceoff circle for a quick snap shot over the left shoulder of Luongo, off the crossbar and in.
Notes: Vancouver also added F Chris Higgins from Florida in a separate trade Monday, but he has a broken thumb and is expected to miss at least another 10 games. ... Kesler's assist was his second point in six games after 13 in the previous 13. ... The Blue Jackets continue their five-game road trip with games in Edmonton on Thursday and Calgary on Friday, the first of five sets of back-to-back games among their final 20. ... The Blue Jackets came in with multiple power play goals in four straight games — and nine overall in that stretch — for the first time since 2002, but were blanked on four attempts by the Canucks' third-ranked penalty kill.