Gerardo Martino's side battled from two goals down to beat the Yellow Submarine 3-2 and stay in the Primera Division title race on an emotional night for the team, who were playing their first game since Vilanova succumbed to throat cancer at the age of 45 on Friday.
"This was one of the most difficult days to play," midfielder Xavi told the club's website. "We felt it in our bodies. We've lost a leader. He will always be an example.
"We relied on our pride and grit to win this game. We dedicate it to Tito."
The night began with a moment of remembrance with Vilanova's image shown on the big screens in tribute to the man who guided the Catalan club to the title in 2013.
Barca were subdued for much of the first half and trailed to a Ruben Cani goal scored on the stroke of half-time.
Manuel Trigueros then doubled the lead 10 minutes into the second half, but two Villarreal own goals sparked a comeback as Gabriel Paulista and Mateo Musacchio inadvertently brought things level before Lionel Messi struck the decisive blow seven minutes from time.
Argentinian centre-back Javier Mascherano said after the game: "Each one of us are getting on in our own way. Everything is so fresh, and the only thing we can do is stand by his family and try to share their pain."
He went on to share happy memories of Vilanova, adding: "Tito always treated me phenomenally well, and whenever we won a title I would hug him and thank him for the experience.
"What we have to do is fight until the end like Tito. We have a lot of fight left in us. We know that his battle was a hard one, but we never could have imagined that this would happen, until it did."
Midfielder Andres Iniesta said: "The death of Tito has really affected us. We knew him for a very long time. With him we won the league with a points haul of 100 points, but what we'll remember about him is what he gave us on a personal level."
Sunday's win left the defending champions four points behind leaders Atletico Madrid with there games left.
"The game we are playing wasn't a bad one," the Spain international added.
"We were in control and we were creating chances, but their goal just before the break hurt us and their second one did as well. But we fought until the end - that's what we had to do and we finally managed to score the go-ahead goal.
"If this team wins, it's because we do a good job, we play football well, we managed to fight back in a very complicated game.
"We have hope that we can win the league, but we don't depend on ourselves. We're clear that we cannot lose any more points, and if the other teams don't lose points the only thing we can do is congratulate the champions."