Crawford made several tough stops but benefited from another tight, disciplined effort by defending Stanley Cup champion Chicago. He lost a bid for his first shutout this season with 8:47 left in the third period when Nashville's Sergei Kostitsyn scored a power-play goal on a deflection.
Dave Bolland and Bryan Bickell also scored for the Blackhawks, who allowed just two Nashville power plays. Chicago has been short-handed only three times in its past three games.
Four of Skille's six goals this season have come against Nashville.
Crawford made his 10th start in the Blackhawks past 12 games and outdueled Nashville rookie Anders Lindback, who finished with 31 saves in his ninth straight start.
Nashville suffered its second straight regulation loss following an 8-0-2 streak.
Lindback was backed up by veteran Pekka Rinne, who returned to the Predators' active roster after missing eight games after having an arthroscopic procedure on his left knee.
Bolland scored the only goal of the first period, with 7:31 remaining, following a bad pass by Lindback.
The goalie tried to fire the puck quickly up the right wing boards to Nashville defenseman Kevin Klein, but the pass was picked off by Chicago's Fernando Pisani. He passed to Bolland, who was alone in front of the net and beat Lindback after deking him to the ice.
Skille's power-play goal midway through the second made it 2-0. After taking a pass from Bolland, Skille's shot from the right circle went off Lindmark's glove, clanked off the right post and landed in the net.
Crawford made several of his best saves in the second. Among them were a pad stop on Joel Ward 3:40 into the period, a block of Cal O'Reilly's drive from the slot just after Skille's goal.
Skille made it 3-0 at 9:14 of the third period on a quick, screen shot from the high slot.
Kostitsyn ended Crawford's shutout bid just under two minutes later by deflecting in Martin Erat's low shot during a power play.
Bickell completed the scoring with 2:32 remaining.
Notes: Crawford has one career shutout, earned in March 2008 against Anaheim during a callup from the minors. ... Kane missed his seventh game with an injured left ankle. Hossa sat out his 10th game with a lower-body injury, but has resumed skating. ... Chicago LW Viktor Stalberg missed his third game with concussion-like symptoms. ... Nashville C David Legwand missed his 15th game with a lower-body injury. ... Predators RW Jordin Tootoo and D Alexander Sulzer were healthy scratches.