Goals from Lionel Messi and Xavi earned the visitors a 2-0 lead before a late Javi Guerra strike gave Pucela hope of salvaging a result, only to see Christian Tello seal victory deep into stoppage time.
The Barcelona players wore t-shirts before the game with "Animo Tito" written across them in tribute to their trainer and, speaking after the game, Xavi stressed that the health of Vilanova was on everyone's minds.
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"We want to dedicate the win to Tito," the 32-year-old midfielder told journalists.
"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."
The league leaders have now stretched their impressive form to 16 wins from 17 La Liga fixtures this campaign 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 currently sit top of La Liga with 49 points, nine clear of closest rivals Atletico Madrid.