Filip Forsberg and Gustav Nyquist scored, and Ryan McDonagh had two assists for the Predators (47-30-5), who had won two in a row and three of four. Juuse Saros made 34 saves.
Nashville, which played its final game of the regular season, remained three points ahead of the Vegas Golden Knights for the first wild card from the Western Conference. Vegas has two games remaining.
“Thought we would ease ourselves into the game. Can't do that,” Predators coach Andrew Brunette said. “I think it's good for our group to realize that's going to be the pace and the atmosphere you're going to face (in the playoffs). I thought the last two periods we got to our game. We were knocking on the door.”
Michael Bunting appeared to give Pittsburgh the lead with a power-play goal at 6:23 of the first period, but it was overturned after Nashville successfully challenged for goaltender interference.
Crosby then gave the Penguins a 1-0 lead at 7:02 after scoring on the same power play. A shot from Bunting snuck five-hole on Saros and sat in the crease, and Crosby came from behind the net to tap it in before McDonagh or Dante Fabbro could clear it.
Karlsson made it 2-0 at 13:50, scoring on a one-timer from the point off a pass from Crosby.
Kris Letang appeared to score past a screen from Lars Eller at 16:20, but Pittsburgh had its second goal overturned after Nashville again challenged for goaltender interference.
“At this time of the year, especially in the position that we are, we can't really look back on things,” Letang said. “We have to just keep looking ahead."