It was Nabokov's second shutout this season and 36th of his career.
Mike Grier's first-period goal turned out to be all offense the Sharks needed but Devin Setoguchi and Joe Thornton added two goals apiece. Thornton, who has a team-leading eight goals, also logged an assist, while Patrick Marleau notched two as San Jose won its second game a row.
Mikael Tellqvist made 23 saves as Phoenix sustained its second straight loss after winning two in a row.
The Coyotes' best chance to get on the board came at 8:22 into the game when Joe Pavelski missed on a penalty shot.