Maxime Talbot added a goal and an assist, and Matt Cooke also scored for Pittsburgh, which improved to 14-2-3 under interim coach Dan Bylsma.
Ryan Callahan, Brandon Dubinsky and Nik Antropov scored for New York, which is 1-2-1 in its past four.
Crosby extended his personal scoring streak to 15 games with the winning goal, his 29th. He took a pass from Ruslan Fedotenko while in the neutral zone and went up the ice with speed, splitting New York defensemen Wade Redden and Derek Morris and beating Henrik Lundqvist with a wrist shot to give Pittsburgh its third lead of the day.
The Penguins took an early 2-0 lead with goals 2:23 apart midway through the first period. Talbot scored his 11th 8:57 in shortly after a power play for Pittsburgh expired. Cooke then got his 10th on a second rebound during a scrum in front of the net, slapping it over Lundqvist - who was sprawled out on the ice.
The Rangers scored twice in final 1:32 of the period to tie it.
Callahan got his 20th by scoring moments after a faceoff win by Scott Gomez and set up by Sean Avery.
Dubinsky then tied it with 4.4 seconds left with a wraparound goal, his 10th.
Fedotenko gave Pittsburgh the lead again 4:14 into the second when he finished a two-on-one with Jordan Staal. The play was started when Pittsburgh defenseman Rob Scuderi "saved" a shot by Gomez that had gotten behind goalie Marc-Andre Fleury.
But the Rangers tied it again with 4:44 left in the period on Antropov's rebound goal, his 27th of the season and sixth in 12 games with New York.
Notes: Counting the playoffs, Pittsburgh is 13-0-2 in its past 15 home games against the Rangers. ... The home team won all six games in the season series. ... Antropov has five goals this season against Pittsburgh, more than any other team. ... Avery has nine points in 12 games since rejoining the Rangers early this month.
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