Joe Pavelski and Andrew Desjardins each scored 3 win over Phoenix.
Last season saw the Sharks finish with 105 points and the team made it to the Western Conference Finals, but fell to the Vancouver Canucks.
Saturday's opener saw the team also get goals from Michal Handzus and Ryane Clowe while Thomas Greiss made 26 saves for San Jose, which has finished with at least 100 points in five straight seasons.
Phoenix made the playoffs for a second straight year lasts season, but were swept in the first round by Detroit.
Due to the ongoing financial problems that the team still faces, the Coyotes lost several key members to free agency, including goaltender Ilya Bryzgalov and defenseman Ed Jovanovski.
Shane Doan scored two goals while Oliver Ekman-Larsson scored the other goal for Phoenix, which got 44 saves from Mike Smith.