Crosby is the eighth-fastest player to reach the milestone, putting him in elite company.
Everyone in the list's top 10 except Crosby and Jaromir Jagr - who's not yet eligible - is a Hall of Famer.
"It's a nice number," Crosby said postgame. "I wasn't thinking about it at the time. Tonight was a big game and we were just focused on getting a win. ... I guess it's a sign I've been playing for a pretty long time, too. It's always nice to get those milestones."
Crosby's longtime rival, Alex Ovechkin, reached the 1,300-point mark March 16 in his 1,177th career game.