Vancouver's Matt Cooke scored midway through the third to tie it one-all and set up overtime. The win moved the Canucks into first place in the Northwest Division.
Chicago's Patrick Sharp opened the scoring early in the third. Blackhawks goalie Patrick Lalime stopped 28 shots.
Lalime, who missed the first half of the season following surgery to repair a herniated disc, made just his second start and appearance. He shut out the Canucks 3-0 in his first start, at Vancouver on Feb. 7.
Chicago outshot Vancouver 11-10 in the first. Luongo made several tough stops, including a sprawling glove save on Denis Arkhipov 3:40 in and a point-blank pad save on Patrick Sharp in the final second of the period.
The Blackhawks misfired - or failed to get off shots - on several close chances early in the second.
Lalime made a tough glove save on Daniel Sedin at 7:39 of the period. He stopped a deflection by Sedin during a Canucks power play just over two minutes later.
Sharp scored at 5:13 of the third on a play off a faceoff in the left circle in the Vancouver zone.
Directly from the draw, Chicago's Martin St. Pierre fired a shot on Luongo. Sharp pounced on the rebound in the slot and beat Luongo from 15 feet.
Chicago's Martin Havlat fired high and missed a half-open net nine minutes into the third.
Cooke tied it one-all with 9:33 left in the third when his low shot from the top of left circle was screened by Chicago defenceman Brent Seatbrook and beat Lalime.
Vancouver's Cooke and Kevin Bieksa failed to convert a two-on-one break 2:15 into overtime.
Luongo stopped Havlat on a breakaway with a second left in overtime.
Notes: Vancouver C Jan Bulis sat out his third game with a shoulder injury. ... Canucks C Tommi Santala and Marc Chouinard were healthy scratches. ... Chicago D Jassen Cullimore was a healthy scratch for the fifth straight game. LW Tony Salmelainen also was a healthy scratch.