The Sharks grabbed home-ice advantage after finishing seventh in the Western Conference. Vancouver will host Game 2 on Friday.
Niemi, who backstopped the Chicago Blackhawks to the Stanley Cup title three years ago and whose 24 wins this season tied him for the league lead, made 30 saves.
Logan Couture tied it on the power play with 3:25 remaining in the second period and Boyle's key goal came 9:17 into the third. Patrick Marleau delivered some insurance for the Sharks with 5:23 to go.
Roberto Luongo allowed all three San Jose goals on 28 shots.