Greiss stopped all six shots he faced in the tiebreaker, and Ryane Clowe scored the lone shootout goal in the sixth round to lift the Sharks to their seventh consecutive victory, 3-2 against the Phoenix Coyotes.
"I was used to the shootout from the AHL," said Greiss, making his eighth appearance of the season. "I just tried to focus in the same way."
Phoenix saw its franchise-record 10-game winning streak snapped.
"We were fortunate to get out of the game with a point," Coyotes coach Dave Tippett said. "We had a good burst of energy early, had shots but not a lot of quality. Then they started competing at a level where we didn't get to."
"Give credit to their goalie," Upshall said. "He played well and their penalty kill was strong."
San Jose held Phoenix scoreless on six power-play chances, four in the second period.
"This was a prime example of gutting out a victory," Sharks coach Todd McLellan said. "We challenged our team today. We wanted to find out how tough we were mentally, how tough we were when things are not going our way with travel and we're not feeling well."
Boyle tied it at 2 with a power-play goal with 14:31 left, taking a blind pass from Clowe on the right doorstep and squeezing a shot between Ilya Bryzgalov's glove and the right post.
"He made a good pass," Boyle said. "I actually wanted to go upstairs but I missed it a little. There was a lot of luck on my side."
Phoenix's Robert Lang had the best scoring chance of overtime, bouncing a shot off the right post with 2:48 remaining.
"We didn't play well enough by any means," Coyotes captain Shane Doan said. "The first period we had a jump but after that they kind of got their legs and got going."
Huskins opened the scoring at 2:53 of the second period with his first goal in 26 games. He shot a rolling puck from the left point over Bryzgalov's blocker.
Pyatt capped a 2-on-1 break with Peter Mueller by scoring from the inside hashes of the left circle to make it 2-1 at 7:42 of the period.
- Sharks C Scott Nichol left the game briefly in the third period when he was cut by Ed Jovanovski's stick while on his knees just inside the Sharks blue line. "I'll take a broken nose for getting the puck out of the zone," Nichol said.
- The Coyotes have played three consecutive shootouts, winning one. Phoenix also saw a shot deflect off the post in overtime of their shootout loss Monday in San Jose.
- Joe Pavelski, who had the second assist on Boyle's goal, has four goals and three assists in his past seven games.
- Coyotes C Vernon Fiddler (lower body) and D Jim Vandermeer (upper body) were out of the lineup for the second successive game.
- Upshall's goal was his first in four games after scoring three times in his previous two.
- Phoenix RW Peter Mueller assisted on Pyatt's goal for his 100th NHL point.