Brady Skjei and Vladislav Namestnikov scored 1:16 apart in the third period, and Alexandar Georgiev made 36 saves for the Rangers (32-36-14), who did not qualify for the playoffs. They lost three of their final four games (1-2-1).
Ryan Strome scored on a snap shot from the left face-off circle at 2:09 of overtime.
"I just thanked [the players] for their effort," Rangers coach David Quinn said after his first season as an NHL coach ended. "I said this before the game, this has been a great group to coach. Obviously not the season we wanted to have and certainly not the record we wanted to have. We certainly want to be playing past this point next year, but they gave it their all. It's a good group to coach. They were attentive. Just proud of the way this ended."
Crosby gave the Penguins a 1-0 lead at 6:36 of the first period. Guentzel passed under Rangers defenseman Neal Pionk's stick to Crosby in the right face-off circle, where he scored on a one-timer for his 35th goal of the season.