The Sharks made it 2-0 at 7:23 of the first period with their first power-play goal. Hertl redirected Matt Irwin's shot past Smith. Tyler Kennedy set up the score when he won the faceoff and Brent Burns kept it alive.
"He had his number," Sharks captain Joe Thornton said. "The first one was beautiful and the second one he was in the right position. Another good game for Tomas. You know he's a world-class goaltender and you have to make your shots count."
Marleau scored his second goal of the season, also on the power play, at 12:30 of the first. Joe Pavelski's shot bounced off Smith's pad and Vlasic was in position to give Marleau an open net.
Phoenix scored at 16:47 of the second period. Ekman-Larsson picked up the puck from Zbynek Michalek in his own zone and carried it all the way, taking a quick shot from the right that glanced into the net off Niemi's right glove.
Couture added an empty-net goal in the final 25 seconds.
The Sharks have beaten Phoenix in 10 of the past 12 meetings in San Jose.
NOTES: The Coyotes, who play six of their first eight games on the road, head to the East Coast to play four games over the next week. ... Phoenix backup goalie Thomas Greiss, who played with the Sharks last year, received a warm reception from the crowd when he was shown on the big screen. ... The Sharks outshot Phoenix 18-8 in the first period.