GLENDALE, Ariz. -- Coming off a dramatic victory in their home finale, the San Jose Sharks had a chance to move closer to earning home-ice advantage in the first round of the playoffs.
They let the opportunity slip through their fingers thanks to a shaky first period and some stingy goaltending by the Phoenix Coyotes' Mike Smith.
Smith stopped 33 shots, and the Coyotes prevented San Jose from moving up in the Western Conference standings with a 2-1 win over the Sharks on Wednesday night.
"Last night was an emotional game, and you're always concerned about guys getting off to a good start," Sharks coach Todd McLellan said of San Jose's win over Dallas on Tuesday. "It took a little while for us to get our legs going and decide to play the way we needed to play. Just not enough tonight."
San Jose scored two goals 30 seconds apart in the third period to beat Dallas 3-2 on Tuesday and clinch its ninth straight playoff appearance. The Sharks had a chance to move ahead of the Los Angeles Kings for fourth in the West after L.A. lost to Minnesota.
Whether it was fatigue from playing back-to-back nights or a lapse in focus, the Sharks stumbled out of the gate against the Coyotes, allowing two goals in the first period.
San Jose was better after that, creating some good chances and pulling within 2-1 on Brent Burns' goal in the second period, but it couldn't get anything else past Smith. The Sharks remained tied with the Kings at 57 points.
Thomas Greiss stopped 30 shots in his first start since March 6 for the Sharks, who will close the season against the defending Stanley Cup champion Kings in Los Angeles on Saturday.
"Mike Smith is just a great goalie, and you saw it again tonight," Sharks captain Joe Thornton said. "A couple plays where we thought it was going to go in, and it just didn't."
Despite being eliminated from the postseason the night before, the Coyotes played like the team fighting for a playoff spot.
Phoenix had the extra jump early, getting goals from Michael Stone and Keith Yandle in the first period. Even when San Jose fought back, the Coyotes didn't buckle, playing the tight-checking style that had been so successful the previous three seasons.
Smith was back in form after allowing three goals to Detroit on Monday. Captain Shane Doan had a pair of assists for Phoenix, which has two games left.
"I thought we would play well," Coyotes coach Dave Tippett said. "I know everybody's disappointed and that room is as disappointed as everybody else, but I know the leadership that Shane Doan has and he's not going to let this team back off.
"I wasn't worried about our commitment to playing hard tonight or whether we were going to go through the motions."
It was a strange position for the Coyotes, who faded down the stretch this season after making late-season pushes to reach the playoffs in previous years.
Phoenix stumbled with a franchise-record goal-less streak of 245 minutes, 32 seconds -- 133 straight shots without a goal -- in mid-March to fall out of the top 10 in the Western Conference and never fully recovered.
The Coyotes' slim playoff chances took a huge hit Monday, when they were shut out for the eighth time this season in a lackluster 4-0 loss at Detroit.
They officially had a run of playoff appearances end at three straight seasons with Minnesota's win over the Kings.
The Coyotes looked like a playoff team in the first period, generating some good chances and a pair of goals.
Stone scored midway through the period when he was left open as all the other players from both teams crammed near the left boards. Taking a pass from Radim Vrbata, Stone sent a slap shot from the right circle under Greiss' stick arm for his fifth of the season.
Yandle made it 2-0 with his 10th of the season from nearly the same spot, one-timing a pass from Oliver Ekman-Larsson on a shot that skipped past Greiss after appearing to hit a Sharks player in front.
"It could have just been from playing last night and traveling, but they got off to a good start," Thornton said. "After the first 20 [minutes], we played solid, but we pretty much gave them the game the first 20 minutes."
Burns cut Phoenix's lead to 2-1 early in the second period, whipping a shot past Smith after a turnover by Ekman-Larsson in the Coyotes' end. It was San Jose's first goal against Smith in more than 200 minutes
The Sharks ramped up the pressure in the third period, but Smith turned away 13 shots, including a couple of tough chances in the closing seconds to seal Phoenix's only-for-pride victory.
"It showed what kind of character we have in here," Smith said. "It wasn't the easiest of games to get up for, we don't like to be in the situation we're in, but there's two ways to look at it: Go out there and feel sorry for yourself and just get through a game, or you could show some pride and play like we did tonight.
"It was a nice way to get a win."
The Coyotes were without D Derek Morris (lower body) and C Rob Klinkhammer (upper body). ... Greiss got the start after Antti Niemi started the previous 24 games. ... A group of Ekman-Larsson fans painted their faces like the Swedish flag and wore jerseys that were half Coyotes, half Swedish national team. Ekman-Larsson is from Karlskrona, Sweden. ... Phoenix will play its final home game Friday against Colorado before finishing the season at Anaheim on Saturday.