For the first time in two decades, the Washington Capitals are heading to the Stanley Cup Final, where they will face this year's Cinderella team, the expansion Vegas Golden Knights.

The Caps punched their ticket by defeating the Tampa Bay Lighting 4-0 on Wednesday night in the seventh game of their Eastern Conference Final series. Vegas had previously eliminated the Winnipeg Jets in the Western final.

Washington let Tampa Bay know early that it meant business: Alex Ovechkin scored the opening goal during the second minute of play. Andre Burakovsky added two more in the second period to help lead the Caps' victory.

"The first goal was very important," said Ovechkin, who will be playing in his first Final. "After that you could see we have all the momentum on our side. Holts [Washington goalkeeper Braden Holtby] was unstoppable today. He was special. Everybody was all in. Everybody was sacrificing their bodies. I think we all deserve the win."

It’s the first time Washington has advanced to the Stanley Cup Final since 1998, when the Caps were swept by Detroit.

Before Wednesday night’s victory, Ovechkin had never made it past the second round during his 13-year career.

"I think Ovie has been on a mission," Capitals coach Barry Trotz said. "They wanted this game, no question."

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The Washington Capitals celebrate their Game 7 Eastern Conference Final victory Wednesday night over the Tampa Bay Lightning. (Associated Press)

Holtby made his presence felt during the winner-take-all showdown, stopping 29 shots and handing the Lightning, who led the NHL in goals during the regular season, their second straight shutout.

The Lightning did not score a goal in the last 159 minutes, 27 seconds of the series – a stretch of nearly eight periods.

Washington beat Tampa Bay three times on the road to secure their spot in the Final against the Golden Knights, improving to 8-2 away from home this postseason.

After Ovechkin’s early score, Burakovsky – who played two games in the first round against Columbus before sitting out 10 straight with an upper-body injury – added a goal on a breakaway against Andrei Vasilevskiy at 8:59 of the second period to become the 17thplayer to score a goal for Washington in the playoffs this year -- four shy of the NHL record.

The winger scored again on another breakaway to give the Capitals a 3-0 edge heading into the final period, with Nicklas Backstrom adding a goal on an empty-netter to complete the rout.

Ovechkin described Wednesday’s faceoff as probably the "biggest game in my life."

"What a game. What an experience. We had a lot of guys pitching in," winger T.J. Oshie said. "The biggest guy of all had to be Holts. He played fantastic, back to back shutouts."

Tampa Bay lost its first two games in the series, but fought back to win three straight and take a 3-2 lead. But, the Capitals proved to be too much in Game 6, shutting out the Lightning 3-0 and pushing the series to a winner-take-all matchup on Wednesday -- which yielded a similar result as Washington kept its foot on the gas.

The Lightning had several missed opportunities to score in Game 7, as a couple shots rebounded off the post and Yanni Gourde failed to get his stick on a loose puck in front on an empty net. The team’s last goal came 33 seconds into the second period of Game 5, which the Lightning went on to win 3-2.

"We're here to win as team, no matter who gets the credit," said Holtby, the fifth goalie to deliver a Game 7 shutout to clinch a spot in the Stanley Cup Final.

"I felt we could have won every game," Lightning coach Jon Cooper said. "We ran into a tough Washington team that was probably feeling the same thing, and once you get this far you've probably done some magical things on the way."

It was the 33rd time a Game 7 matchup determined who advanced to the Stanley Cup Final, with the Home team 21-12 in those situations.

Tampa Bay also played Game 7 in the Eastern Conference final in 2015, when they blanked the New York Rangers, and again two years ago, when they lost 2-1 to Pittsburgh.

Both of those deciding games were on the road. The Lightning had never lost a Game 7 at home before Wednesday night.

"It's going to take a few days to digest this. It's tough to sit here right now and think of positive things and how it was a pretty great season," Lightning captain Steven Stamkos said. "It doesn't seem that way when you have this group — and we've been to this position before — and you can't find a way to give yourself a chance a win. We thought we had that group. It's just an empty feeling right now."

Now, the Capitals set their sights on the Golden Knights, who hope to cumulate their prolific inaugural season run by hoisting the Stanley Cup trophy.

"I feel very happy, but we're not finished yet," Ovechkin said. "We've been waiting for this moment a long time."

An expansion team hasn’t made it to the Final since 1968, when the St. Louis Blues beat out five other NHL newcomers to win the West Division, as it was then called.

The Knights went 2-0 against the Capitals in the regular season, winning 3-0 at home on Dec. 23 and 4-3 at Washington on Feb. 4.

Game 1 of the Stanley Cup Final will be played in Las Vegas on Monday night.

The Associated Press contributed to this report.