[WATCH: All Capitals vs. Golden Knights highlights | Complete Golden Knights vs. Capitals series coverage]
Eller had a goal and two assists for the Capitals. Alex Ovechkin and Brooks Orpik also scored, Andre Burakovsky had two assists, and Holtby made 37 saves, including a reaching stick save on Alex Tuch from the slot with 1:59 remaining.
"It was a great save," Washington coach Barry Trotz said. "You could see the emotion on our bench. Once he made that save, I knew we were going to win the game."
James Neal and Shea Theodore scored, and Marc-Andre Fleury made 23 saves for the Golden Knights.
It was the first win in the Cup Final in Capitals history.
Game 3 of the best-of-7 series is at Washington on Saturday.
"Nobody said it's going to be a 4-0 series," Vegas center Erik Haula said. "It's going to be ups and downs. We've been here before. We've been good on the road. Just put this behind, learn from your mistakes, just try to do things better, and that's it."
Video: WSH@VGK, Gm2: Eller pots Kempny's nice pass
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."
[RELATED: Holtby save draws raves from Capitals | Fleury, Golden Knights stay confident]
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.
Video: WSH@VGK, Gm2: Ovechkin delivers check on McNabb
Goal of the game
Ovechkin's goal at 5:38 of the second period.
Video: WSH@VGK, Gm2: Ovechkin buries PPG on nice setup
Save of the game
Holtby stopping Tuch at 18:01 of the third period.
Video: WSH@VGK, Gm2: Holtby reaches for unreal stick save
Highlight of the game
Orpik's goal at 9:41 of the second period.
Video: WSH@VGK, Gm2: Orpik scores on fortuitous deflection
They said it
"We feel comfortable at any point in a series. That's one of the beautiful things of our group, but this is a tough place to win in Vegas and it's shown throughout the League. To come away with a split, it's good, but now we move forward. We need to take advantage of our own rink, our own familiarity, and focus on Game 3 because this game is gone now." -- Capitals goalie Braden Holtby
Video: WSH@VGK, Gm2: Holtby on stellar save, Game 2 victory
"We didn't play our best game, but I thought we had 39 shots and we still created a lot. It's one of those games where Holtby played real well, he was probably the difference in the hockey game." -- Golden Knights coach Gerard Gallant
Video: WSH@VGK, Gm2: Gallant talks chances after 3-2 loss
Need to know
Ovechkin scored 116 goals, regular season and playoffs included, during Orpik's 220-game goal drought. … The Capitals were swept by the Detroit Red Wings in their only other Stanley Cup Final appearance, in 1998. ... The Golden Knights have scored the first goal in all nine of their home games this postseason, with each goal coming in the first period, including six in the first eight minutes.
Game 3 of Stanley Cup Final at Capital One Arena on Saturday (8 p.m. ET; NBCSN, CBC, SN, TVAS)
Video: Caps earn first Cup Final win, even series with Vegas
Stanley Cup Final Coverage
Golden Knights vs. Capitals
Stanley Cup Final Schedule