Duchene tied it 1-1 at 18:49 after taking a stretch pass from Mikael Granlund. Pittsburgh defenseman Marcus Pettersson fell, sending Duchene in on a breakaway for his NHL career-high 38th goal of the season.
Crosby had two of Pittsburgh's three shots in the first, when it was outshot 11-3.
Nick Cousins gave the Predators a 2-1 lead at 4:31 of the third with a wrist shot from the high slot. He had three assists in his previous 12 games.
"I thought it was a good game," Cousins said. "I think overall, it was a pretty even game. They just make a play in overtime. We'll take the point and move on to our five-game homestand."
Jason Zucker tied it 2-2 at 8:53 on a backhand set up by Crosby. It was his first goal since scoring twice against the Golden Knights on Jan. 17, his final game before missing the next 30 because of core muscle surgery.
NOTES:Crosby is the 22nd player to reach 1,400 NHL points and third active, joining Florida Panthers forward Joe Thornton (1,538) and Capitals forward Alex Ovechkin (1,403). He is the seventh-fastest to reach the mark, behind Wayne Gretzky (580 games), Mario Lemieux (691), Marcel Dionne (1,022), Phil Esposito (1,070), Jaromir Jagr (1,086) and Steve Yzerman (1,093). … Predators goalie Juuse Saros is day to day with a non-COVID illness after making 21 saves in a 4-1 loss to the Florida Panthers on Saturday. Connor Ingram was recalled from Milwaukee of the American Hockey League and backed up Rittich. … Nashville defenseman Mark Borowiecki did not play the third period after taking a stick to the face from Penguins forward Evgeni Malkin at the end of the second. There was no update following the game.