Skinner netted the winner with 3:31 left on a shot from the right wing that slipped under goalie Carter Hutton's pads for his team-leading 20th goal. He has scored six times during the winning streak.
"We're just trying to keep this thing going right now," Skinner said. "We're being consistent in our game and playing solid for all 60 minutes."
Patric Hornqvist had tied it for Nashville with a power-play goal at 6:46 of the third period when he tipped in the puck at the right post for his ninth goal. But the Predators, who had earned points in four straight games, dropped their third in a row.
The Hurricanes took a 1-0 lead on Semin's goal 4:28 into the game. Semin gathered the puck from behind the net and sent a shot in off of Hutton's back.
Nashville coach Barry Trotz wasn't pleased with either goal allowed by Hutton.
"I thought we really held them down to no chances," Trotz said. "We got zero saves. (Skinner's goal) wasn't much of a shot at all."
The Predators will now return to Nashville for a five-game homestand after an 0-3 trip.
"We should have had five or six points out of this trip," Trotz said. "We came away with two, and that's discouraging. We put ourselves in the position to get points, so we just need a save."
Staal sat out after he sustained a lower-body injury Saturday night in a win at the New York Islanders. He could be sidelined for a few more days.
Nashville, which avoided its first shutout against the Hurricanes, held a 32-25 shots advantage. The Predators went 1 for 2 on the power play and killed Carolina's two man-advantages.
Khudobin, filling in for Ward, improved to 5-0 this season and helped the Hurricanes win both ends of a back-to-back set for the first time this season.
"It wasn't easy at all," Khudobin said. "I was just doing my job, trying to stop the pucks. We know the situation right now with every game being important."
Khudobin started his third straight game after missing 33 because of an ankle injury. Muller said it was a risk to go back to him after Khudobin's 38-save effort against the Islanders.
"We took a chance, three in four nights for him, but he's been playing well," Muller said. "We just went for it."
The Hurricanes, in their third game in four nights, played well without Staal in the lineup. Staal, who missed his first game since Feb. 26, 2011, had played in 191 consecutive regular-season games -- the third longest streak in franchise history. He holds the team record of 349 straight games.
Skinner extended his point streak to five games. ... The Hurricanes activated D Jay Harrison from the injured list and placed Ward on it, retroactive to Dec. 31. ... Hornqvist moved into a tie for seventh place on the Predators' career goal list.
Copyright by STATS LLC and The Associated Press
Arena: PNC Arena Location: Raleigh, North Carolina
Referees: Don VanMassenhoven, Mike Leggo Linesmen: Derek Amell, Bryan Pancich