World Player of the Year Lionel Messi netted twice and Spain Under-21 midfielder Thiago Alcantara was also on the scoresheet for Barca in their bid for a club record-equalling fourth consecutive Spanish title.
The victory was an impressive response to title rivals Real Madrid after Jose Mourinho's side inflicted a 6-0 demolition on Real Zaragoza on Sunday when Portuguese forward Cristiano Ronaldo scored a hat-trick.
The 24-year-old, who also scored from a Messi assist in Barca's 2-0 European Super Cup win over Porto on Friday, was at the Catalan club's youth academy with the Argentina forward and the pair already look to have created a formidable partnership.
"Cesc knows his team-mates very well," Guardiola said at a news conference. "He has a very big and strong personality. He was the captain of an important team."
Messi grabbed a second and Barca's fifth when he turned in Alcantara's fine centre with 15 minutes left.
La Liga kicked off a week late at the weekend after the first round of matches fell victim to a strike called by the players' union (AFE) over unpaid wages. The dispute with the league (LFP) was finally resolved on Thursday.
Villarreal's defeat and a shaky performance on Saturday from Valencia, the other two Spanish teams in this season's Champions League, suggests it will again be a straight fight between Barca and Real for the title.
Villarreal coach Juan Carlos Garrido noted at his post-match news conference that Barca and Real's domestic dominance was due to them being so much richer than their La Liga rivals.
Barca's annual budget was just under 430 million euros last season compared with less than 70 million at Villarreal.
"Today we
