Malkin put Pittsburgh ahead 1-0 on one of its two shots in the second period at 13:49, banking a wrist shot from behind the net off the stick of Michael McCarron and in off the back of Saros for his fourth goal this season.
Nashville was unable to score on two breakaways.
Erik Haula had a short-handed chance at 8:51 of the first period, but was denied by Silovs with a right pad save.
Justin Barron left the penalty box and went backhand to forehand twice before Silovs fell forward and extended his left pad for a save at 7:33 of the second.
"I've been around the game a long time," Predators coach Andrew Brunette said. "I still believe when you do things a certain way, you get rewarded. ... Today, you know, the consistency and the commitment of playing a certain way, we have to play a certain way. We stayed with it. That was the one thing the last few games we kind of got away from."
Pittsburgh failed to get a shot on goal on its two power plays.
"We just didn't execute well," Crosby said. "We weren't in our spots. We were disorganized. I don't know if it's from a bit of a layover or not playing in a few days, but it's not what we've done all year. So, it's unfortunate."
NOTES: Forsberg is the 12th Sweden-born player to score a goal in an NHL regular-season game in his home country. He factored on a game-tying goal for the 135th time in the NHL, passing Roman Josi (134) for the most in Predators history. ... The Penguins and Predators are the first two NHL teams to compete head-to-head in multiple regular-season games overseas. They opened the 2000-01 regular season against each other with GAME ONe Japan 2000 in Saitama, Japan. ... Pittsburgh is 2-2-1 in regular-season games outside of North America; Nashville is 4-1-0. … Malkin (39 years, 106 days) is the oldest player in League history with a goal during a regular-season game outside North America. Rob Blake (37 years, 293 days) previously held the mark from the 2007 Premiere Series opener at O2 Arena in London, England.