Soriano netted for the home side with a sweet strike that curled into the top corner after 64 minutes. Valencia pushed forward in the second half but could not find an equaliser.
Fourth-placed Villarreal's fourth straight league win gave them 33 points from 17 games.
There are plenty of problems, however, for Valencia with Neville having been brought in with the target of winning a place in the Champions League.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
They are now 10th on 22 points with two draws and a defeat in the league under the former Manchester United and England player.
"It went in perfectly and where the keeper couldn't reach it," Soriano told reporters. "We knew it would be a difficult game with Valencia defending deeply but we have confidence at the moment and created chances."
Barcelona, who have a game in hand, are level with Atletico Madrid at the top of the table on 38 points. Real Madrid are third with 36 points.
Valencia have injury problems and Neville opted for a solid formation with a five-man defence, and Alvaro Negredo and Paco Alcacer together in attack for the first time.
There was little connection between the forwards as Villarreal controlled possession in midfield but the visitors did manage to hinder their build-up play.
Jonathan Dos Santos had a snap shot comfortably saved by Valencia keeper Jaume Domenech and Soriano had a free kick that whistled just wide.
Valencia went more on the front foot after the break, with Alcacer firing over when well placed in the area, but it was Villarreal who struck the only goal.
Alcacer went on to miss another good opening and Neville's men were unable to mount any concerted pressure.
(Editing by Tony Jimenez)
