Atletico Madrid's bid to bounce back from a heavy Champions League defeat fell short as Real Sociedad rescued a 1-1 draw thanks to Luka Sucic's brilliant late strike.
Lewandowski reached 10 goals for the season in nine league games, stretching his lead as the division's top goalscorer with a first-half treble.
Champions Madrid beat Villarreal on Saturday to pull level with Barcelona but the Catalans strolled to a comfortable triumph at Alaves' Mendizorroza stadium to continue a strong start to the campaign under new coach Hansi Flick.
"I get a lot of good passes and so it's easier for me to score goals," Lewandowski told DAZN.
"Today in the first half we played well from the first minute, we wanted to attack and score goals.
"If you score three goals in the first half then in the second you can play with everything under control."
Barca secured their eighth victory in nine La Liga matches by taking control from the start.
Lewandowski and winger Raphinha, in superb form this season, were Barcelona's key players in a match they largely dominated.
The Brazil international had a goal disallowed for offside before setting up Lewandowski for the opener with an inviting free-kick, which the striker headed home.
Raphinha burst down the left wing for Barcelona's second, crossing for the veteran Polish forward to knock in.
Lewandowski completed his hat-trick with a clinical finish across Sivera after collecting Eric Garcia's pass.
The 36-year-old hitman looks far sharper than last season and has 12 goals in 11 games across all competitions.
"In front of goal (Lewandowski) is the best player, for me," Flick told reporters.
"It's amazing to score so many goals over such a period... I'm really happy with him and you can see he's 100 percent fit, it's perfect at the moment.
"I'm happy for Lewy but also the other team-mates are really supporting him very (well)."
Alaves had goals from Toni Martinez and Santiago Mourino ruled out for offside as they battled well in the second half but Barca held firm.
Atletico denied
Diego Simeone's Atletico were thrashed 4-0 by Benfica on Wednesday but took a first-minute lead in San Sebastian against Real Sociedad.
Former Manchester City striker Julian Alvarez drilled home after Antoine Griezmann's cute backheel into his path.
The Rojiblancos battled hard defensively to keep their advantage but Sucic looped a long-range effort over Jan Oblak in the 84th minute to secure the home side a point.
Atletico's point took them third, level with Villarreal, but they trail leaders Barcelona by seven, while Real Sociedad are 15th.
"We scored the goal, the team worked well defensively, we didn't allow a team that plays well (to create) much danger," Simeone told DAZN.
"Look at their goal, a great strike, and that's about it, I think a draw was fair."
Sevilla shaded a derby clash against Real Betis 1-0 while Girona snatched a late 2-1 win over Athletic Bilbao.
Dodi Lukebakio's penalty was enough to pull Sevilla up to 12th, level on points with derby rivals Betis.
The winger converted from the spot in the 50th minute after a handball by Diego Llorente, who was furious with the decision.
"I just ask for respect, we work like mad every week and there are referees who lie to our faces," said Llorente, who said the referee had claimed the defender's arm was in a raised position.
Veteran Sevilla winger Jesus Navas, 38, played in his 28th and final Seville derby, becoming the player with the most appearances in the fixture -- one more than Betis great Joaquin.
Earlier Girona snatched a late win over sixth-placed Athletic Bilbao in an entertaining clash.
Cristhian Stuani converted a late penalty to earn three points for last season's surprise package, who are currently 11th after a difficult start this season.
Girona goalkeeper Paulo Gazzaniga saved two penalties, denying Alex Berenguer and then Ander Herrera.
