SAN JOSE, Calif. -- With an outside shot at the division title and home ice in the first round, Milan Lucic took matters into his own hands Thursday night.

The Edmonton power forward scored a third-period natural hat trick to lead the Oilers to a 4-2 win over the injury-depleted Sharks, a team they will face to open the postseason next week if they don't catch the Pacific-leading Anaheim Ducks.

"You throw the three goals out, even," Edmonton coach Todd McLellan said. "His physicality, his ability to keep plays alive, power-play execution, I thought he was tremendous. We're lucky to have him at this time of the year. That's exactly what we brought him in for."

Lucic scored his 21st, 22nd and 23rd goals, two on power plays and one at even strength. Defenseman Oscar Klefbom provided assists on all four Edmonton goals as the Oilers moved two points ahead of San Jose with their sixth win in seven games.

San Jose (45-29-7) was eliminated from Pacific Division title contention when Anaheim beat Chicago earlier in the evening. Edmonton (46-26-9) has an outside shot at catching the Ducks, but it is unlikely.

The Sharks, held to a season-low 15 shots while Edmonton blocked 28, could pass the Oilers but only if they beat Calgary on Saturday while Edmonton loses consecutive games in regulation to lowly Vancouver on the weekend.

"We would have loved to win this game and have a chance to secure home ice on Saturday," Sharks forward Jannik Hansen said. "Now it's out of our hands. With that being said, home ice is home ice. You've still got to win the games."

Lucic redirected Klefbom's drive from the right point past Sharks goalie Martin Jones (28 saves) at 4:26 of the third, just seven seconds into a power play awarded for San Jose having too many men on the ice.

Then, Lucic scored again at 7:57 by gaining position in front of San Jose defenseman David Schlemko to tap in a Klefbom feed after the visitors broke on 3-on-2. And Lucic capped the scoring with a power-play strike at 16:31.

"The last three games, pucks just find me in the right place and I'm able to pounce on it," Lucic said. "You kind of look around New Year's time, where nothing is really going for you and you're getting frustrated because nothing is bouncing your way. Then you start working to the right places and working the right way and eventually it starts going in for you."

Edmonton's Connor McDavid extended his points streak to 12 games by scoring a goal and adding an assist to bring his NHL-leading total to 97 points.

The teams traded goals in the second period as San Jose nursed a 2-1 lead into the third despite getting outshot 21-10.

Edmonton tied the game at 4:40 when McDavid tapped in his 30th goal on a weak-side rebound to cap a long Oilers cycle against a tired San Jose unit. Klefbom's shot from the left point struck both Tomas Hertl and Justin Braun before caroming off the left pad of Jones right to an unmarked McDavid.

"We felt like we played a pretty good game, we just didn't find a way to win," Schlemko said.

Held to just six shots for the first 30 minutes, the Sharks broke back on top when Brent Burns scored his on-going career-high 29th goal at 12:30.

Hertl helped San Jose win an offensive-zone draw taken by Mikkel Boedker by tapping the puck to Burns at the points. Lucic darted toward Burns, but was unable to block the defenseman's wrist shot that beat screened Edmonton goalie Cam Talbot (13 saves).

"It's tough in those games when you don't see a lot but when you do see them they had some good looks," Talbot said. "I was just trying to stay focused and make those saves because those chances can change the momentum of the game."

The Sharks scored the only goal of the opening period, and despite getting outshot 10-5, the hosts dominated the first 20 minutes.

Edmonton was on its heels early when forced to kill consecutive penalties -- a too-many-men minor and a David Desharnais slash of Hansen.

But just four seconds after Desharnais exited the box, San Jose scored when Joel Ward tipped a Schlemko shot from the middle of the blue line through the legs of Talbot at 6:08. Ward's second goal in as many games gave him 10 to become San Jose's seventh double-figure goal-scorer.

"It's frustrating we let a game get away from us, one we felt we had pretty good control," Sharks captain Joe Pavelski said. "It was right there, it felt good all night, even with the shot total, it just didn't feel like that."

NOTES: San Jose's top two injured centers -- Joe Thornton (left knee) and Logan Couture (mouth) -- participated in a morning skate for the second straight day but continued to be sidelined. Thornton has missed two games, Couture six, and both are termed by coach Peter DeBoer as day-to-day. ... Each team made a change to their fourth lines as Oilers RW Iiro Pakarinen subbed in for Anton Slepyshev while San Jose LW Micheal Haley replaced rookie Timo Meier. ... Edmonton G Cam Talbot earned his 41st win of the season to break Grant Fuhr's franchise record of 40 set in 1988-89. ... Edmonton D Kris Russell had nine blocked shots. ... Sharks F Marcus Sorensen was denied on a penalty shot at 2:19 of the third period after Oilers D Matt Benning dragged the breakaway rookie down from behind with a horse-collar hook.