The veteran Polish striker’s treble helped Hansi Flick’s side capitalise on Madrid’s 0-0 draw earlier on at Rayo Vallecano.
Teenager Lamine Yamal also scored for Barca in another gripping game produced by the champions’ attacking approach, and Marcus Rashford produced two more assists.
Frenkie de Jong was sent off late on for Barca for two yellow cards but by then the champions had secured their victory.
Flick insisted Barcelona would not change their style despite some recent struggles, including a 3-3 draw with Club Brugge in the Champions League on Wednesday, and it led to a wild first half.
The champions nosed ahead through a Lewandowski penalty on 10 minutes after Marcos Alonso handled Fermin Lopez’s shot, but Celta equalised a minute later.
Rashford missed a one-on-one chance after Lopez sent him through and Celta broke away to score.
The Galicians capitalised on Barcelona’s high defensive line, sending Sergio Carreira scampering in behind and he held his nerve to beat Wojciech Szczesny.
Without Pedri, Raphinha and Joan Garcia, among other injured players, Flick called on his team to show more fight in their absence and they seemed more energised at Balaidos.
Ilaix Moriba blocked Lopez’s shot, Rashford turned the rebound against the post and Celta stopper Ionut Radu denied Lewandowski from close range as he followed up.
Looking back to his best, Lewandowski grabbed his second from an inviting Rashford cross to put Barca back in front on 37 minutes. His shot slipped past Radu, who might have done better.
Celta quickly hit back again, this time through Borja Iglesias, who smashed a rocket over Szczesny and into the back of the net from the edge of the box two minutes before the interval.
However, Barca went in with the lead when Rashford’s deflected cross found teenage star Yamal, who beat Radu at his near post. (AFP)
