Jonathan Cheechoo and Matt Carle also scored, and Joe Thornton added three assists for the Sharks, who won for the fifth time in six games.
Shane Doan scored for the Coyotes, losers of two straight after a seven-game winning streak.
Clowe broke a 1-1 tie at 14:28 of the second period when he one-timed Doug Murray's pass from the left boards over Curtis Joseph's left shoulder for his eighth goal in five games.
Carle made it 3-1 just 51 seconds into the third when he gained control of a long rebound near the left end line and slipped the puck behind Joseph. Cheechoo added a power-play goal with 9:31 remaining, redirecting Christian Ehrhoff's shot from the point.
Clowe had given the Sharks an early lead on San Jose's third and final shot of the first period, taking a pass from Thornton in the low slot and scoring off a quick wrist shot.
Clowe has 11 goals and three assists in 21 games.
Phoenix tied the score with a power-play goal at 9:41 of the second. Ladislav Nagy passed the puck behind the net to Steven Reinprecht. When San Jose defenceman Kyle McLaren left Doan to cover Reinprecht, the Coyotes' centre fed the puck to Doan on the top left edge of the crease for the goal.
The Coyotes were held to one shot on goal in the first, an attempt from Doan from the right faceoff circle with 46 seconds to go in the period.
Notes: San Jose leads the season series 3-2, winning the first two meetings and losing the next two before Saturday's win. ... Coyotes C Jeremy Roenick, who recorded a hat trick against the Sharks in Phoenix's 8-0 win on Dec. 30, was a healthy scratch. ... Thornton's first assist was the 400th of his career and 600th point. ... Doan has eight goals and five assists in his last nine games. ... Coyotes D Nick Boynton returned to the lineup for the first time since Nov. 25 and C Patrick Fischer was playing for the first time since Dec. 12. Boynton had been out with a fractured foot, Fischer with a strained groin.