The Penguins had a 2-0 lead on goals by Rust (1:53) and Sheahan (2:48) in the second period, but the Rangers responded in the third with goals from Kreider on the power play at 8:42 and Fast to tie the game at 2-2 with 5:32 left.
Hagelin gave Pittsburgh a 3-2 lead with a wraparound goal with 4:19 remaining, but Zibanejad scored on the power play 62 seconds later to tie the game 3-3. Kreider made a move around Letang and set up Zibanejad with a crossing pass for a tap-in from the right post.
Malkin was awarded the penalty shot with 11 seconds remaining because the officials ruled that Georgiev knocked the net off its moorings intentionally in the final two minutes. Georgiev, who said he didn't do it on purpose, made a right pad save after trying to stop Malkin with a poke check.
"I just wanted to be patient with him, wait for his maybe first, maybe second, third move," Georgiev said. "Wait for his [move], not go down really early. I think I was patient with that."
Zibanejad scored the winner after getting a backhanded pass from Kreider between the circles. He carried the puck through the right circle and beat DeSmith with a short-side shot.
"We totally ruined it," Letang said. "We had a great first two periods and we got too confident and didn't respect them enough. They came back in the third and we were sloppy."