Lewandowski scored from close range on the stroke of halftime and then netted a penalty four minutes into the second half to give Hansi Flick a winning start as Barca coach, Xinhua news agency reported.
Valencia took the lead in the 44th minute of an even first half when Hugo Duro headed Diego Lopez's cross from the left wing.
Pau Cubarsi cleared an effort from Duro off the line moments later after Marc-Andre ter Stegen had given the ball away. After being inches away from going 2-0 down, Barca were level.
Alejandro Balde was given space to cross from the left and Lamine Yamal knocked his ball across the six-yard box for Lewandowski to level, and Lewandowski scored the winning goal after Raphinha had been clipped inside the Valencia area.
Earlier in the day Osasuna and Leganes drew 1-1, with Juan Cruz putting newly promoted Leganes ahead with an excellent goal after 22 minutes, only for bad luck to deny them a win after Aimar Oroz's ball off the post hit Leganes defender Juan Soriano to bounce into the net.
The season kicked off on Thursday night when Athletic Club Bilbao drew 1-1 at home to Getafe while Real Betis and Girona drew by the same score.
Celta Vigo came from behind to win 2-1 at home to Alaves on Friday and Las Palmas came from behind twice to take a point with a 2-2 draw at home to Sevilla.
