Couture broke a scoreless tie 6:20 into the second period on a power-play goal after Montreal's David Desharnais was whistled for hooking Matt Nieto.
San Jose doubled the advantage early in the final period when a dump-in pass by Patrick Marleau took a strange bounce off a stanchion and came right to Couture, who fired it past a stunned Carey Price.
Niemi stopped all 22 shots he saw for his second whitewash in three games and the 25th of his career for the Sharks, who bounced back after a 2-1 loss at Boston Thursday.
Price finished with 35 saves for the Canadiens, who fell for the third time in four games.
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