The Alicante-based minnows CF Intercity play in Spain's third tier and were not given a chance against a Barca side full of internationals ahead of the game.
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Soldevila, though, had other ideas and netted three times against the club he played for as an under-18 before leaving for England.
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Barcelona went into the clash top of LaLiga, against a 16th-placed Intercity who were only formed five years ago, and ply their trade in the Primera Federacion.
It did not matter, as 21-year-old forward Soledvila, who previously spent two campaigns with Birmingham City's development squad, had the game of his life.
Barca took the lead through Uruguayan defender Ronald Araujo, and to the delight of the 'home' supporters.
The ground only holds 1,000 season ticket holders, and playing it at Hercules' stadium meant it was full of Alicante-based Barca fans.
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On 58 minutes, Barcelona-born Soldevila scored and stunned everyone in the ground, making it 1-1.
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After Xavi made several changes, Barca were back in front with Ousmane Dembele scoring his sixth goal of the season.
However, the drama did not stop, Soldevila was on hand again, getting ahead of Jordi Alba to head home, making it 2-2.
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Alba made up for his poor defending, though, and picked out ex-Leeds United forward Raphinha who but the Catalan's on course for victory.
But that wasn't all, Soldevila was at it again, and sealed his hat-trick by beating Barca shot-stopper Inaki Pena at his near post - whilst taking the game to extra-time.
Soldevila's three goals made him the first player to net a hat-trick since Kylian Mbappe in February 2021, when Paris Saint-Germain won 4-1 at the Camp Nou in the Champions League.
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Intercity rallied on, but Ansu Fati secured the win in extra-time for Barcelona, to ensure Xavi's men avoided an banana skin, to win the match 4-3, and book their place in the last-16 of the Spanish Cup.