Of Holtby's 15 saves in the third period, nine came in a span of 2:52 with the Capitals killing overlapping penalties.
Only one of those saves came during 68 seconds of 5-on-3 time for the Golden Knights, who lamented blowing the opportunity to tie the game on the two-man advantage.
"We just need to be more selfish and shoot the puck," forward Jonathan Marchessault said. "The plays were there."
Neal gave Vegas a 1-0 lead at 7:58 of the first period when he beat Holtby with a shot from the left face-off circle.
The Capitals scored the next three goals, all after losing center Evgeny Kuznetsov for the rest of the game
because of an upper-body injury he sustained on a hit
by Golden Knights defenseman Brayden McNabb with 5:21 remaining in the first period.
Trotz said he had no update on Kuznetsov following the game.
"It's a tough break there, but I felt like we came together really as a team," Washington center Nicklas Backstrom said. "We tried to play better than we did the first 10 minutes. We kept it simple. It's all about commitment too. We blocked shots and we played for each other."
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Eller moved up to the second line after Kuznetsov was injured and replaced him on the top power-play unit.
"He's a guy who is kind of our secret weapon," Washington captain Alex Ovechkin said.
Eller tied it 1-1 at 17:27 of the first from the bottom of the right circle off a pass from defenseman Michal Kempny. It was his sixth goal of the 2018 Stanley Cup Playoffs.
Then, from Kuznetsov's position as the low forward on the power play, Eller set up Ovechkin for a power-play goal from the bottom of the left circle to give the Capitals a 2-1 lead at 5:38 of the second.
Eller then made the pass to Orpik, who gave Washington a 3-1 lead on a wrist shot from the right circle at 9:41 of the second.
It was Orpik's first goal in 220 games, including 39 in the postseason, dating to Feb. 26, 2016. It was his first goal in the playoffs since April 21, 2014, for the Pittsburgh Penguins, a span of 55 games.
"I screamed, ears are still ringing," Capitals forward T.J. Oshie said. "He's one of those old-school pro guys. I've only played with three or four of them. He's one of those guys, and to see him get rewarded on the scoresheet, it's exciting."
Theodore scored on the power play to make it 3-2 at 17:47 of the second, but Holtby stopped the final 16 shots he faced.
"Thank God he's our goalie," Ovechkin said.