Colin Wilson scored with 24.3 seconds remaining in the third period and Rinne made 39 saves to give the Predators a 3-1 victory over the Washington Capitals.
In the final minute, Martin Erat carried the puck below the goal line, pulling Washington's Vokoun with him.
Erat calmly slid the puck to Wilson, who had an open net to tap the puck into for his fourth goal of the season.
"There was literally just inches for Marty to make that play," Wilson said. "He hit me there and Vokoun was out. That's just a good job by Marty."
The Predators have won four of six. Washington has lost four of its past five.
"This is a tough one to take," Washington coach Bruce Boudreau said. "I thought for 56 minutes we played as good as we could play. We scored the goal and in the last two periods we totally, I thought, dominated, and then we scored the goal to take the lead and we stopped playing."
After two scoreless periods, Washington's Troy Brouwer opened the scoring with a wrist shot from the high slot that sailed over Rinne's right shoulder at 15:14.
Just 28 seconds later, Erat tied the game at 1 with a tap-in from the left post off a cross-crease feed from Nashville captain Shea Weber. Weber added an empty-net goal with 20 seconds remaining.
Vokoun, who was with the Predators from 1998-2007, made 28 saves.
"We score that goal, we basically, we can only blame ourselves," Vokoun said. "We give them the win. It's not much else you can say. I think we play pretty good overall, but you get a 1-0 lead five minutes left in the game or whatever, you can't give up plays like that. I really don't know what to say."
The Capitals had a good scoring chance late in the first period.
With the Capitals on a two-man advantage, Nicklas Backstrom sent a pass from below the goal line to Brooks Laich in the low slot where his point-blank chance was turned aside by Rinne.
Making things worse for Nashville was that its top defensive pairing of Weber and Ryan Suter were the penalized Predators at the time.
"It was just one of those desperation things," Rinne said. "When you play 5 on 3, especially with their skilled guys like Backstrom, you always expect them to make those backdoor and one-time plays. Luckily I was able to make a few good saves."
Rinne stopped Laich again with 9:11 remaining in the second.
John Carlson caught the Predators on a bad line change and sent Laich on a partial break on the left side. Laich pulled up at the top of the left circle and fired a slap shot on goal that Rinne stopped.
Laich had a game-high seven shots on goal Tuesday.
"Their dangerous guys were getting chances and that was really concerning," Nashville coach Barry Trotz said. "I loved the way we responded. Our big time players stepped up tonight."
Vokoun made a spectacular save late in the second period. Washington was on another power play and had the puck in the Predators zone, but Nashville center Mike Fisher took the puck the other way on a breakaway. Vokoun stopped Fisher's forehand with his outstretched left pad keeping the game scoreless.
Capitals D Mike Green missed his second consecutive game and eighth of the past nine. ... Washington played its first of three consecutive road games against teams from three different divisions. The final two games on the trip will be played in Winnipeg and Toronto. ... The game was Nashville's second of three consecutive against Eastern Conference opponents.
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NASHVILLE, TN - NOVEMBER 15: Defenseman Shea Weber, right, of the Nashville Predators laces up his skates for...