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Borja Iglesias's hat-trick looked to have put the visitors in control, but Hansi Flick's substitutions made the difference for Barca, before Raphinha's stoppage-time penalty proved the difference.

Barcelona took the lead when Ferran Torres picked up the ball in midfield and found space to dribble towards goal, pulling the trigger from the edge of the box to beat Vicente Guaita for his 10th league goal of the season.

But Celta responded immediately when Pablo Duran put in a superb cross from the wing. Wojciech Szczesny missed the ball after sprinting off his line, leaving Iglesias with a tap-in into an empty net.

Barcelona then went behind seven minutes into the second half, when Frenkie de Jong made an error and completely missed a long ball, allowing Iglesias to run through and beat Szczesny to grab his second goal.

As the hosts pushed forward to find an equaliser, a Celta clearance found Iglesias again, and he capitalised on the home side's high line to sprint through on goal and beat Szczesny for a third time to claim his hat-trick.

A stunned Barcelona responded two minutes later, getting one back in the 64th minute when Robert Lewandowski, who limped off injured shortly after, and Raphinha combined to find Dani Olmo, who scored five minutes after coming on as a substitute.

Four minutes later, Barcelona levelled it at 3-3 when Lamine Yamal, another substitute, crossed the ball into the six-yard box where Raphinha rose above the defence to head home.

Celta looked set to leave with a point, but Olmo was fouled in the box and earned a stoppage-time penalty after a video assistant referee check, with Raphinha stepping up to blast the ball into the top corner in the 98th minute to snatch the win.

The result puts the pressure back on Real Madrid, which plays fourth-placed Athletic Club on Monday (AEST). Celta Vigo is seventh with 43 points.