After losing the first three games of the Western Conference quarterfinal series, the Blackhawks outscored the top-seeded Canucks in the fourth and fifth contests by a combined score of 12-2.
Chicago will host Game 6 Sunday and a Blackhawks win in that one would force a deciding showdown in Vancouver Tuesday.
Hossa opened the scoring 5:54 into the game with a power-play goal and Keith tallied his first of the contest just 24 seconds later. Patrick Kane made it 3-0 before the first period was over and both Hossa and Keith added second-period tallies.
Crawford, in his first full season with the Blackhawks, appeared in only his sixth playoff game. He stopped 37 shots.
Roberto Luongo allowed four goals on a mere eight shots before being replaced in the second period by Cory Schneider.