ANAHEIM, Calif. -- After winning Game 6 of their Western Conference quarterfinal series Monday night, the Nashville Predators saw a message in their locker room:

"Noon flight to Anaheim. Pack for six days."

Colin Wilson, Paul Gaustad and Pekka Rinne ensured those instructions would remain relevant.

Wilson and Gaustad scored in the first period as the Predators eliminated the Anaheim Ducks from the Stanley Cup playoffs with a 2-1 victory in the seventh game of the series Wednesday night in front of a standing-room-only crowd of 17,407 at the Honda Center.

Rinne stopped 36 shots for the Predators, who will face the San Jose Sharks on Friday night in the first game of the conference semifinals after winning the best-of-seven series against Anaheim, 4-3.

"I was able to see most of the shots," Rinne said. "Defensively, I thought we did an excellent job. Sometimes, you have to win games like that."

Ducks left winger Andrew Cogliano agreed.

"Tonight was probably one of our best offensive games in the series, if not the best," Cogliano said, "but they gutted it out. They're a tough team to play against in their own end because they cut cycles off.

The victory came in the first Game 7 in Predators history.

"It's a big step," Nashville coach Peter Laviolette said. "If you don't take this step, you can't take any more steps."

Ryan Kesler scored the only goal for the Ducks, who received 18 saves from goalie Frederik Andersen yet failed to win a seventh game for the fifth time since 2009. For the fourth consecutive year, opponents eliminated Anaheim in a Game 7 while the Ducks served as the home team.

"We were playing catch-up the whole game, the whole series and all year," Ducks center Ryan Getzlaf said. "It came to bite us at the end."

Anaheim coach Bruce Boudreau admitted that this loss in a Game 7 contained a stronger sting.

"With the way the score was and the way we were pushing, I'd say yes, especially with how hard we had to push from November just to get to where we were," Boudreau said. "We did everything the hard way."

Rinne prevented the hosts from taking the lead about four minutes after the opening face-off, when he did the splits while making a lunging catch of Cam Fowler's slap shot from the blue line.

Wilson put Nashville ahead 6:19 into the game with his second goal of the playoffs. Defenseman Mattias Ekholm flipped a high pass from the left boards in the Predators' zone to Wilson at the Ducks' blue line.

Wilson tried to feed a pass between Anaheim defensemen Simon Despres and Clayton Stoner to Mike Fisher. Despres blocked the high pass with his glove and deflected the puck to the ice. However, before Despres could play the puck, Wilson stole it and propelled a backhand inside the right post.

"Those flipped-up pucks are hard to control for the defensemen," Wilson said. "I was just trying to wait. With the way 'Fish' was going, pushing him back, I was fortunate enough for it to come up on my stick."

That goal tied Wilson with Martin Erat for fourth place on the Predators' all-time playoff goal-scoring list with eight.

Gaustad's second career playoff goal and first in the series extended the lead to 2-0 at 15:53. With his stick at shoulder level, Gaustad deflected Shea Weber's slap shot from the right point under the crossbar. Boudreau challenged the call, which video replay upheld.

Nashville needed the crossbar to keep the Ducks scoreless early in the second period. After Rinne blocked Rickard Rakell's tip-in, Jamie McGinn tried to convert the rebound with Rinne prone on the ice. However, McGinn's shot hit the crossbar about five minutes into the period.

"We knew they were going to make a push after we were up 2-0," Predators defenseman Roman Josi said. "But the defense was amazing tonight. They've got a great cycle game and pass it to the points, but our forwards did a great job getting in the shot lanes."

Kesler ended Rinne's quest for a shutout on a power play 1:45 into the third period. The center one-timed a shot in front of the crease off Jakob Silfverberg's pass from behind the net for his fourth goal.

Anaheim came close to scoring the tying goal with about seven minutes to play. Hampus Lindholm fired a shot from the blue line that deflected off the back of Rinne's glove and slowly trickled off the left post before Rinne covered it with his glove.

"It came down to seven games for a reason," Weber said. "Everything about it was a battle, a fight. I guess it was only fitting it was that close in the end, as well."

NOTES: Wednesday night marked the first time since April 1974 that a Stanley Cup quarterfinal and semifinal game took place on the same date. The New York Islanders beat the Tampa Bay Lightning in Game 1 of an Eastern Conference semifinal Wednesday. ... Nashville scratched RW Gabriel Bourque (upper body), C Cody Bass (lower body), D Petter Granberg, LW Eric Nystrom and LW Austin Watson. ... Predators D Shea Weber needs one goal to tie David Legwand for the team lead in career playoff goals. Weber amassed 12 in 52 games. ... Anaheim scratched D Josh Manson (head), LW Brandon Pirri (upper body), D Korbinian Holzer, C Mike Santorelli, D Shea Theodore and C Chris Wagner. ... Ducks D Clayton Stoner made his first appearance since the regular-season finale April 10. A hip injury caused Stoner to miss the past six playoff games. ... Ducks RW Corey Perry made his 97th playoff appearance, tying Francois Beauchemin for the second most in team history.