Kane, the NHL's first overall draft pick in 2007, had two goals and an assist to lead Chicago to a 4-1 victory Sunday night.
Andrew Ladd and Patrick Sharp also scored for Chicago, which is 7-3-0 in its last 10 games.
With three points, Kane retook the NHL rookie scoring lead. He entered the game tied with idle Washington's Nicklas Backstrom with 52 points.
Although depleted by injuries - six Blackhawks regulars sat out - Chicago dominated the Canucks with aggressive play. Chicago managed 28 shots, while holding Vancouver to a season-low 10.
"Every win is huge," Kane said. 'We'll try to do things the right way to get in (to the playoffs). From defense comes offense, like the last goal today."
The Blackhawks are six points out of eighth place and the final playoff spot in the Western Conference. The Canucks are in a three-way tie for eighth in the West.
"We had everybody going," Chicago defenseman Duncan Keith said. "Defensively we were doing the little things."
"It was a big game and we stepped up," Blackhawks coach Denis Savard added. "We stuck to our gameplan. There were barely any turnovers and we finished our checks."
Ryan Kesler scored for Vancouver, which lost its third straight (0-2-1), but first in regulation in nine games. The Canucks entered the contest with points in each of their eight previous games, going 5-0-3.
"They wanted it more than we did," Canucks captain Markus Naslund said. "They came out hard and we didn't respond to them at all.
"Ten shots on goal? That's embarrassing," he added. "Considering where we are, we should be more desperate than they are."
Canucks coach Alain Vigneault agreed.
"They came to play," he said. "They played hard, they were physical and they were the better team on the ice."
Chicago's Patrick Lalime made his fifth straight start in place of the injured Nikolai Khabibulin (back spasms).
Vancouver's Roberto Luongo blocked 22 shots in his 14th straight start before being replaced by Curtis Sanford at 9:49 of the third period.
"Maybe it's best that we just forget about his one," Luongo said.
Chicago outshot Vancouver 9-2 in the first and took a 1-0 lead on Ladd's goal with 2:58 left.
From the edge of the crease, Ladd knocked in a rebound of Kane's shot. Kane set up the play when he stole the puck from Canucks defenseman Willie Mitchell in the Vancouver zone, turned and drove to the net through traffic.
The goal was Ladd's second in three games with Chicago since being acquired from Carolina last Tuesday.
Kane's power-play goal at 4:19 of the second made it 2-0. His screened shot from the slot bounced past Luongo's right side.
Kesler cut it to 2-1 with 1:29 left in the period during a 4-on-4.
Sharp made it 3-1 at 5:27 of the third, scoring on a mid-air deflection of Keith's shot from the left point.
Kane extended it to 4-1 with his second goal at 9:24 of the period. He knocked in a rebound of Ben Eager's shot out of the air at the right side of the crease.
Notes: With Khabibulin out, Lalime was backed up by Corey Crawford. Besides Khabibulin, Chicago regulars sitting out with injuries were: LW Martin Havlat (shoulder); C Robert Lang (back) D Brent Sopel (wrist); C Yanic Perreault (wrist; and C Kevin Adams (knee surgery). Adams has resumed skating. ... The Blackhawks will determine this week whether Havlat's injury is season ending. ... Chicago recalled forwards Bryan Bickell and Jacob Dowell from Rockford of the AHL in time for Sunday's game. ... Out for Vancouver were C Brendan Morrison (wrist) and D Lukas Krajicek (shoulder). Veteran Canucks C Trevor Linden was a healthy scratch.