The Canucks will face Nashville in the second round while the Blackhawks will not be around to defend their Stanley Cup championship.
Burrows grabbed a turnover in the Blackhawks zone and ripped a slap shot from the right circle that beat Chicago goaltender Corey Crawford at 5:22 of the OT period.
The goal was the second of the night for Burrows. His goal at 2:43 of the first period stood up until 1:56 remained in regulation. Chicago's Jonathan Toews scored a short-handed goal that tied the score 1-1.
Crawford finished with 36 saves. Vancouver's Roberto Luongo had 31 saves.