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.
Fan wears 'Forced Sex University' shirt to insult FSU on Saturday
18-year-old elf alleges mall Santa pinched her buttocks on the job