After Sunday's Clasico defeat and virtual elimination from the Champions League, the Catalans and coach Xavi Hernandez were desperate to prove a point at Camp Nou.
Lewandowski, the top scorer in La Liga, extended his domestic tally to 11 goals and his brace, along with Ansu Fati's strike, came in an eight-minute blitz near the end of the first half which effectively killed the game.
Xavi made five changes from the side which lost to Real Madrid, most notably dropping Sergio Busquets and deploying Frenkie de Jong in the pivot role, where he excelled.
"After the bad results against Inter Milan and Madrid, we needed to win, Villarreal is a good team, 3-0, and a good victory," De Jong told Movistar.
"If you win games, it always helps, the atmosphere in the dressing room is much better, I'm very happy with the victory.
"I don't care where I play, I feel comfortable in any position."
Women's Ballon d'Or winner Alexia Putellas presented her trophy to Camp Nou before kick-off, and Barcelona could have used some of her creativity in the opening stages as Villarreal's defence stood firm.
Arnaut Danjuma had the first chance of note, firing into the side netting after winning space against Jules Kounde. However, the Catalans played their way into the game as De Jong pulled the strings, and with Lewandowski up front, goals are never far away.
Soothing the pain
Just after the half-hour mark Jordi Alba guided Pedri's finely-weighted pass to Lewandowski, whose turn sent two defenders flying out of the picture, and a third flung himself in vain to try and block as the Poland international fired home.
Lewandowski won an award for his scoring exploits on Monday at the Paris gala too, and combined with Kopa Trophy winner Gavi for the second goal.
After being fed by the 18-year-old, voted the best under-21 player in the world, Lewandowski took his time on the edge of the box before arcing a superb strike out of Geronimo Rulli's reach and into the net.
The third was quick to follow, with Ferran Torres setting up Fati, who hit the post with his first attempt but flicked the rebound home from virtually on the goal-line.
Villarreal had let in three goals in their first nine games, then three more goals in an eight-minute spell at Camp Nou, as Barcelona offered a riposte to their critics.
Barca substitute Raphinha should have extended the lead when set up by Ousmane Dembele but fired wide with the goal gaping, while the effervescent Pedri drilled wide.
Former Barcelona coach Ernesto Valverde returns with Athletic Bilbao on Sunday, before the Catalans host Bayern Munich, by which point they might be out of the Champions League, depending on Inter Milan's result against Viktoria Plzen.
Fans chanted Xavi's name in support of the coach, after he had readily admitted his head would be on the chopping block if the club didn't win a trophy this season.
More pain seems inevitable in the Champions League, but this victory at a canter ensures second-place Barcelona remain on Madrid's tail and firmly in the title fight.
There was a moment of silence before kick-off to mourn the death of Villarreal vice-president Jose Manuel Llaneza, who passed away earlier Thursday after a battle with leukaemia.
"The news of Jose Manuel's death affected us because it was him who started this project," said Villarreal coach Unai Emery.
"I spent two intense years with him, he loved Villarreal, the main reason to have pride and motivation was to give him the victory, but in the end it didn't come through in our game because Barca were better."
Elsewhere Almeria edged Girona 3-2 in a thrilling clash, while Osasuna won for the first time in four, beating Espanyol 1-0 at home to go seventh.