Despite Barcelona dominating possession, it was the visitors’ Hugo Duro and Peter Gonzalez who failed to take advantage of early chances.
Valencia were made to rue those missed opportunities midway through the half, when Barcelona took the lead with their first shot on target. Raphinha dug out an accurate cross from the left, which was sent past Mamardashvili by the head of Fermin Lopez.
Barça keeper Marc-Andre ter Stegen had not conceded a home league goal since February, but he allowed Valencia a route back into the contest just five minutes later.
The German raced out of his area and beat Duro to a lofted pass, but sliced his clearance straight to the striker, who rolled the ball into the empty net.
Barça being the architects of their own downfall did not end there however, as Ronald Araújo caught Gonzalez inside the box, allowing Pepelu to slot the resulting penalty down the middle and send Los Ches into the lead.
Araújo almost made amends for his error when he crashed a header against the post in stoppage time, before more late drama.
Mamardashvili miscontrolled a backpass and presented the ball to Lamine Yamal, before using his hand outside the area to stop the youngster from knocking the ball past him. VAR spotted the infringement, leaving the referee no choice but to show the red card.
It took just four second-half minutes for the man advantage to pay dividends for the hosts, thanks to an İlkay Gundogan corner which was flicked on by Lewandowski and past substitute goalkeeper Jaume Domenech.
From then on, the Blaugrana poured forward as Valencia firmly parked the bus, with Domenech keeping out efforts from Araujo, Jules Kounde and Joao Felix.
But in the week in which Xavi made a U-turn on his decision to leave the club, Barcelona completed a turnaround of their own.
Eight minutes from time, another Gundogan corner was not dealt with by Domenech, who punched the ball towards Lewandowski, and the Pole nodded the ball into an unguarded net to regain the lead.
Victory was sealed in stoppage time, as Lewandowski completed his hat-trick by curling a free-kick beyond Domenech.
The win means Barca leapfrog Girona into second place before the two meet next weekend, while Valencia have now lost consecutive matches for the first time since October.
Flashscore Man of the Match: Robert Lewandowski (Barcelona)
