Smith made 33 saves through overtime and then turned aside two more shots in the shootout to carry the Coyotes to a 1-0 win over the Sharks on Saturday.
"It was a good one for me because they throw a lot of stuff at your feet from all different angles, and you have to be sharp all over the ice," Smith said. "It was a good one for me to get under my belt.
"We knew they would come at us pretty hard, and I was fortunate enough to come out on top."
"I thought I would do something else, even when I was in the slot," Vrbata said. "Then the instinct kicked in and I did what I usually do."
Smith, who recorded his second shutout of the season, made several acrobatic saves, including one in the shootout. Smith has 21 career NHL shutouts.
"He was excellent. He made some big saves at the right time," Coyotes coach Dave Tippett said. "He made some tough saves on shots that came through traffic. When you don't give up any goals you give your team a chance to win."
Niemi was nearly perfect, too, stopping 21 shots before the shootout to earn his first shutout of the season and 20th in the NHL.
"We still need to bear down around the net, but there are things we can build upon heading out on the road," Sharks center Joe Thornton said. "We feel comfortable playing this type of game, but unfortunately we lost in a shootout."
Smith improved to 14-19 in shootouts, and Niemi fell to 19-13.
San Jose, which has gone to a shootout in four of six games, dropped its second straight tiebreaker. The Coyotes are 1-1 in shootouts, both coming on the road.
Both teams hadn't won in their previous three games.
The Sharks entered with one power-play goal in their previous 21 opportunities, and went 0-for-4. Phoenix came with four goals in 23 chances before an 0-for-3 performance.
San Jose has turned around its penalty-killing. After allowing a power-play goal in each of their first three games, the Sharks have killed 34 straight short-handed situations.
"I knew our penalty kill has been good but I don't worry about the streak," Niemi said. "Just stopping shots."
The last time these teams met, there was plenty of offense. The Sharks scored three straight goals in a 5-3 win, and Thornton set a team record for the most points (9) in the first three games of a season (1 goal, 8 assists). Patrick Marleau also became the first player in 20 years to open a season with three straight multiple-goal games.
Smith, who shut out the Sharks three times last season, improved to 6-3-1 in his career against them.
Coyotes C Martin Hanzal, who left the game for precautionary reasons, had a four-game point streak snapped. ... Coyotes C Boyd Gordon played in his 450th NHL game. ... The Sharks activated D Brent Burns, who played in his first game of the season. D Matt Irwin was assigned to Worchester of the AHL to make room. ... Tippett coached in his 750th game. ... Sharks LW Ryan Clowe hasn't scored a goal this season.