Lionel Messi opened the scoring yesterday from Luis Suarez's cutback four minutes before the break, but Villarreal levelled shortly after half-time when Marc-Andre Ter Stegen failed to keep out Manu Trigueros's drive.
However, Barca were back in front within a minute through Andres Iniesta and Gerard Pique's header 26 minutes from time made it 3-1.
The Catalans could have had an even healthier advantage to take into the second leg on March 4, but Neymar had his penalty saved by Sergio Asenjo.
"It could have been even better with the penalty we missed, but it is a good result and deserved based on what we saw on the pitch."
Villarreal coach Marcelino meanwhile described his side's evening like a "horror film" having not only lost the match but captain Bruno and former Barca midfielder Jonathan dos Santos to injury.
"This game seemed lke a horror film. Barcelona took advantage of our mistakes and scored the type of goals we didn't expect.
All of Villarreal's good defensive work in the opening 45 minutes was undone four minutes before half-time when Mateo Musacchio slipped to allow Suarez to rob possession and he squared for Messi to slot home his 11th goal in his last nine games.
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