Crosby had a breakaway 55 seconds into overtime, but Samsonov made a pad save.
Nic Dowd gave the Capitals a 1-0 lead with a shorthanded goal at 5:50 of the first period. After intercepting a pass from Penguins defenseman Kris Letang along the blue line, Dowd shot five-hole on a breakaway.
"Honestly, ever since even before I came here, I used to watch these guys play each other," Dowd said. "It kind of just seems like every time we play each other, something weird happens. It didn't surprise me at all that we went back and forth like that. Some guys scored some big goals at big times. And our goaltending was great."
Evgeni Malkin tied it 1-1 on a one-timer during the power play at 6:26, ending Pittsburgh's streak of five games without a first-period goal.
The center has scored 10 points (three goals, seven assists) on a nine-game point streak and at least one point in 10 of 12 games since returning Jan. 11 from offseason knee surgery.
"I try to do my best," Malkin said. "We had a tough schedule the last week. We played so [many] games. But guys play good, unbelievable. Play hard. Try everything. But I know I can play better, and I will."
Vanecek, who was skated into by Penguins forward Kasperi Kapanen, was replaced by Samsonov at 6:43 of the first period. Vanecek allowed one goal on two shots.
Rust gave the Penguins a 2-1 lead at 11:26 with a power-play goal on a backhand.
Orlov tied it 2-2 at 16:13 with a power-play goal on a wrist shot off a rebound.
Rust put Pittsburgh up 3-2 at 4:44 of the second period by tapping in the puck on a power play after Crosby chipped a shot off the post. Rust also scored two goals in a 4-3 loss to the Los Angeles Kings on Sunday.
Dowd appeared to tie it by tipping a shot at 7:05. It was overturned after a Penguins challenge, which ruled Dowd interfered with Jarry.