Goals from Lionel Messi and Xavi earned the visitors a 2-0 lead before a late Javi Guerra strike gave Valldolid hope of salvaging a result. Cristian Tello sealed the victory deep into stoppage time for the unbeaten La Liga leader, though.
Barcelona players wore T-shirts before the game with "Animo Tito" written across them in tribute to the ailing coach, who underwent surgery for a relapse of a tumor in his throat, and, speaking after the game, Xavi stressed that the health of Vilanova was on everyone's minds.
"We want to dedicate the win to Tito," Xavi told reporters. "He’s not going through the best of times, but now he’s home, and that’s great news. The operation went well, and we worked hard to be able to dedicate this victory to him."
Barcelona stretched its impressive form to 16 wins from 17 La Liga fixtures this campaign with the win, and Xavi emphasised the importance of entering the winter break with another victory.
"The result consolidates our spot at the top of the table," the Blaugrana stalwart added. "We’re on a brutal run, and we want to continue on this path. We're physically strong and when we return from the break we want to continue on form."
Barcelona sits comfortably atop of the Spanish table with 49 points, nine clear of closest competitor Atletico Madrid.