Sharks forward Patrick Marleau played the 1,756th game of his NHL career, tying Mark Messier for second place in NHL history. He is 11 games away from tying Gordie Howe's record.
Kessel scored four goals in a sweep of the back-to-back set for the Coyotes (16-14-5), who have won three straight. Clayton Keller had a goal and two assists.
"Phil's an opportunistic guy, a lot of his goals this year have been hacking and whacking in front of the net, and that's good to see," Coyotes coach Rick Tocchet said. "When Phil's doing that, it's a good thing. When he gets on a hot streak, it's good for us."
Kessel has seven goals in four games against the Sharks this season, and nine during a five-game goal streak against them. He has 14 goals in 35 games this season, as many as he had in 70 games last season.
"I haven't changed anything," Kessel said. "I feel like it's going in a little more, and I'm getting a little luckier than last year, and my body's doing better than it did last year. Whenever your body feels good, it helps."
Hill's shutout was the second of his NHL career. His first was Nov. 29, 2018, against the Nashville Predators.
"We're playing the right way," said Hill, who is starting because goalies Darcy Kuemper and Antti Raanta each is out with a lower-body injury. "We're playing detailed and we're playing to our identity."
Hill made 54 saves on 56 shots in the two games against the Sharks.
"I don't think he was overtaxed," Tocchet said. "But I don't care, whenever any goalie plays back to back, it's tough. But he's a big guy with stamina, and we wanted to go right back with him, and I thought he was really good."