Barca moved a step closer to their fourth Copa showpiece in five years with the home success in the first leg of their semi-final.
Lionel Messi gave the Catalan giants a 41st-minute lead, only for Villarreal's Manuel Trigueros to stun the Camp Nou crowd with a brilliant effort from distance just after the break.
Andres Iniesta and Gerard Pique netted in the second half, though, while Barcelona also missed the chance to score a fourth as Neymar's penalty was saved by Sergio Asenjo.
"We have played a very complete game in all phases, against a dangerous team," Luis Enrique is quoted as saying by the club's official Twitter account.
"[It has] not decided the tie and it does not do justice [to us].
"But it is a good result."
Pique added: "We know that [playing at] El Madrigal is very complicated. [But] we are confident."
