Jeff Halpern beat rookie goaltender Johan Hedberg with a one-timer 4:01 into the extra period, giving Washington a 4-3 victory and tying their Eastern Conference quarterfinal series at two games apiece.
After the Capitals scored their first five goals of the series on the power play, Halpern took a feed from Steve Konowalchuk and beat Hedberg through the pads from the right hashmark.
"When (Mario) Lemieux's on the ice and 68's (Jaromir Jagr) out there, you have to keep a defensive posture," Halpern said. "In the overtime, they told us to take a few more chances.
"It's the kind of thing where you thank heaven that the goal went in. I just went out and shot. I just closed my eyes and took as hard a shot as I could."
Konowalchuk, who scored twice before Washington relinquished its first two-goal lead of the series, set up the game-winner by outmuscling defenseman Marc Bergevin behind the net.
"It was nice to get rewarded," Konowalchuk said.
It was the first goal of the series for Halpern, who was held without a shot in the first three games but helped send the Caps home even. They host Game Five on Saturday afternoon.
"Stanley Cup playoffs are what we play for," Halpern said. "It's now a question of going home and coming up with a big effort on Saturday."
Defenseman Brendan Witt also scored for the Capitals, who were 3-for-5 on the power play and are 5-for-17 in the series.
"We don't need to open it up 5-on-5," Konowalchuk said. "We can work for the power-play opportunities. Even strength, just let it happen. We know we can't try to match Pittsburgh goal for goal."
"It could do a little for our confidence that we finally scored 5-on-5," added Caps goalie Olaf Kolzig.
Lemieux, Jagr and defenseman Janne Laukkanen scored for the Penguins, who went 2-for-5 with the man advantage.
Just after Washington's 14-second two-man advantage expired, Halpern threw a pass from Hedberg's right to Konowalchuk in front of the net for a 1-0 lead 7:49 into the game.
Pittsburgh still trailed by a goal before Lemieux scored on a bad-angle shot 75 seconds into the second period. It was his second goal of the series and the 72nd playoff tally of his Hall of Fame career.
After a couple of near-misses by Washington, Witt scored on the power play 44 seconds before the second intermission, giving the Caps a 2-1 lead with his first postseason goal since 1998.
After winding up from the top of the left faceoff circle, Witt put a slap shot past Hedberg, who was chopped by Dainius Zubrus' stick as the puck approached.
"I got slashed on the second goal," said Hedberg, who made his NHL debut in March. "Last year, they would have gone upstairs and waved it off."
Washington took a 3-1 lead 9:09 into the third, when Konowalchuk tipped Sergei Gonchar's slap shot under Hedberg's left pad.
Laukkanen was in the penalty box for holding the stick. He took two minor penalties in the game and Washington scored on both power plays.
"We need a little bit more on our penalty-killing," Lemieux said. "We have to play more disciplined, pay more attention to not getting in trouble."
The Caps had their first two-goal lead of the series, but it did not last long as Jagr and Laukkanen scored power-play goals 2:36 apart.
Jagr followed his own shot and poked a loose puck under a fallen Kolzig 11:14 into the period. He later threw a puck toward the net from the right side and watched it ricochet to Laukkanen, who hit a half-empty net from the left circle.
Kolzig made a couple of big saves in the final minute of regulation and finished with 29. He also watched Jagr shove a puck wide of the left goalpost on a partial breakaway 2:26 into overtime.
"We had a good feeling heading to overtime," Lemieux said. "We certainly had our chances early."
The Penguins now head to Washington, where they have won five of their last six playoff games. They also have knocked the Caps out of the postseason in five of six all-time meetings.
"We're still in the series," Pittsburgh defenseman Darius Kasparaitis said. "I think we've played our strongest efforts on the road. Our games in Pittsburgh haven't been as good. It's an advantage, perhaps, to go on the road."