Crosby scored the equalizer shorthanded in the second period and assisted on Jake Guentzel's go-ahead goal in the third. His empty-net goal sealed the deal in overtime.
"Sid was phenomenal tonight," said head coach Mike Sullivan. "He made some incredible plays and led by example."
The game went to overtime after Charlie Coyle tied the score with just 1:48 remaining in regulation. Crosby then won it with a wrist shot from the slot.
"It was a huge win for us," said Crosby. "We battled hard and found a way to get the job done."
The Bruins were disappointed to lose their streak but appreciated the Penguins' effort.
"They're a great team and they played a great game," said Patrice Bergeron. "We have to learn from this and move on."
The Penguins will host the New York Islanders on Tuesday, while the Bruins will face the Washington Capitals on Wednesday.
Read also:
Christmas Clash: Shaq's Determination To Overlook Kobe's Shadow
Crosby Has 3 Points, Penguins Recover To End Bruins' 4