The Golden Knights' historic inaugural season ended with their first four-game losing streak.
"I think people would have said we would have won 20 games this year, so to find ourselves playing for a Stanley Cup, it's pretty special, but just a little bit short," Vegas forward James Neal said.
"But proud of the guys."
Nate Schmidt, David Perron and Reilly Smith scored, and Marc-Andre Fleury made 29 saves for Vegas, which lost three games in the first three rounds.
"We worked hard tonight, we competed hard, just couldn't beat that team," coach Gerard Gallant said. "They deserved the Stanley Cup."
The Smith-Pelly and Eller goals each came off a Golden Knights turnover in their own zone.
"We left our goalie out to dry," Vegas defenseman Deryk Engelland said.
Smith-Pelly scored while falling into the right face-off circle after kicking the puck to his stick.
It was his third goal in as many games and his seventh in 24 NHL playoff games. He scored seven goals in 75 regular-season games.
Eller scored the winner from the slot, shoveling the puck into the net after it got behind Fleury, who made the initial save on Brett Connolly's shot.
"[Fleury] was so far out I couldn't get in front of him, which is usually where the rebound comes," Eller said. "So I got behind him and the puck just squeaks through. Usually, Connolly shoots between the legs, and it was just at the right place at the right moment."
Vegas scored twice in the final 7:04 of the second period to take a 3-2 lead.
Perron tied it 2-2 at 12:56 after he was pushed into the net by Washington defenseman Christian Djoos. The Capitals challenged for goalie interference, but the goal was upheld after video review when it was ruled that Djoos caused Perron to contact Holtby before the puck crossed the goal line.
Smith gave Vegas a 3-2 lead with a power-play goal at 19:31.
Washington took a 1-0 lead on Vrana's breakaway goal at 6:24 of the second. The Golden Knights tied it 1-1 at 9:40 when Schmidt's shot deflected in off Niskanen's right skate.
Ovechkin gave the Capitals a 2-1 lead with a power-play goal at 10:14.
"I can't explain what I feel," Ovechkin said. "It's unbelievable."
Goal of the game
Smith-Pelly's goal at 9:52 of the third period.
Save of the game
Holtby stopping Tomas Nosek at 1:18 of the third period.
Highlight of the game
Eller's goal at 12:23 of the third period.
They said it
"It was like we were a bunch of 10-year-olds that just won their first hockey tournament. It was like we were a bunch of little kids again. Amazing. Amazing." -- Capitals defenseman Matt Niskanen
"You don't want to finish on a note like that, necessarily. But one thing I know: We'll be back." -- Golden Knights forward Jonathan Marchessault
"I just knew once we got the lead this group was not letting go. This group got angry and mean, and they said, 'It ain't happening.'" -- Capitals coach Barry Trotz
Need to know
John Carlson had an assist on Ovechkin's goal, giving him 55 points (18 goals, 37 assists) in the NHL playoffs, the most by a Capitals defenseman. … Eller is the first Denmark-born player to win the Stanley Cup. … Washington center Evgeny Kuznetsov led the NHL with 32 points (12 goals, 20 assists) in the playoffs. He is the third Russia-born player to do so since 1943-44. (Sergei Fedorov, Red Wings, 1995; Evgeni Malkin, Pittsburgh Penguins, 2009 and 2017). … Ovechkin passed John Druce for most goals for the Capitals in a single postseason. Druce had 14 in 15 games in 1990. Ovechkin's previous high was 11 in 14 games in 2009.
