Fermin was one of four players to come into Barcelona’s starting line-up, promoted after scoring the final goal as a substitute in the 3-0 home win over Levante.
The 22-year-old midfielder pulled the strings, creating the game’s first clear-cut chance for right-back Jules Kounde, who dragged his shot horribly wide of the far post.
Lamine Yamal had a speculative effort held by Villarreal goalkeeper Luiz Junior but made no mistake from his next chance, and created a superb second goal from nothing.
Fermin pounced on a loose ball in midfield before playing in Lamine Yamal, who took a touch before slotting in the opener.
The teenage Spain international then received the ball out on the right wing and beat two defenders before firing high past Junior and inside the far post.
Junior made a point-blank save from Dani Olmo right after half-time and Villarreal halved the deficit moments later, with Gueye converting from close range after a corner fell into his path.
The visitors had won three of their past four games to climb above Atletico Madrid into third place, nine points behind Real, and Ayoze Perez should have drawn them level after 54 minutes.
Barcelona keeper Joan Garcia failed to clear after rushing out to halt a Villarreal counter-attack, leaving two covering defenders between Perez and the goal, but the ex-Newcastle and Leicester forward shot wide from outside the box.
Tempers flared on the sideline, with each team’s head coach booked, before Barcelona’s Hansi Flick brought on Pedri for Olmo.
The 23-year-old Spain midfielder helped the hosts regain control before threading a fine pass through to Lamine Yamal, who beat Junior from a wide angle to reach 13 La Liga goals this season and a combined 101 goals and assists for club and country.
Pedri and French defender Kounde then combined for the latter to square for Lewandowski to tap in his 11th La Liga goal of the season.
