Barcelona's triumph at the Camp Nou was their second come-from-behind win in a row, after they trailed twice against Atletico Madrid on Wednesday to also prevail 3-2 in their Copa del Rey quarter-final second leg.
And Luis Enrique was thrilled to see that kind of persistence up against genuine La Liga rivals in reigning champions Atletico and Villarreal, who sit sixth in the Spanish top flight.
"Coming back twice is important, it shows that the team is on form," the 44-year-old said.
"Today we did it again against a great team."
Villarreal led 1-0 and 2-1 in the Catalan capital with Denis Cheryshev and Luciano Vietto scoring either side of Neymar's strike.
But after Vietto put the visitors in front in the 51st minute, Barcelona responded quickly with Rafinha equalising two minutes later before Lionel Messi struck the winning goal in the 55th minute.
Rafinha's goal was his first in La Liga and Luis Enrique hailed the Brazilian midfielder's performance, claiming he will be a long-term prospect for Barcelona.
"It's a pleasure to have such dangerous players up in attack, and that are on such great form," Luis Enrique said.
"Rafinha has played a very complete game, he'll be very important to us in the future."
The 21-year-old Brazilian was thrilled to have been given just his sixth start in Spain's top division, telling Canal+: "It was a very important match for me.
"I've given everything, although I know it's hard to earn a starting role."
