Xavi opened the scoring after 10 minutes, before Pedro scored twice and Lionel Messi grabbed a goal - all before a third of the Catalunya derby had been played.
The 25-year-old hopes that the Blaugrana's excellent performances can be maintained throughout the 2012-13 season, and he is glad to have Vilanova back on the Camp Nou sidelines too, having been absent since mid-December.
"We wanted to dedicate the victory to Tito and we could do it," the Spain international told reporters.
"He has had a very complicated few days, but the important thing is that it is good and we are happy to have him back with us.
"We have to continue with this mentality. Step by step, game by game. The mentality should be kept up so as not to lose points.
"He [Vilanova] has told us to be calm, we played as usual, we did our game and we were aware of what some of the Espanyol players could do."
Barcelona sits top of La Liga on 52 points, 16 points ahead of last year's winnersReal Madrid, while second-placed Atletico Madrid lost ground on the Catalans after it was held to a 1-1 draw by Mallorca on Sunday.