Fellow countryman Robert Lewandowski contributed two goals in the commanding victory.
Szczęsny, previously with Arsenal and Juventus, had a quiet night in goal as Barça dominated the match, Polish state news agency PAP reported.
The Polish keeper joined Barcelona in early October as a replacement for Marc-André ter Stegen, the German goalkeeper sidelined for the season due to a knee injury.
Lewandowski, meanwhile, netted goals in the 31st and 47th minutes, helping propel the Blaugrana into the last 16 of the Copa del Rey, Spain's oldest football competition.
The 36-year-old forward, who joined Barcelona from Bayern Munich in the summer of 2022, also serves as the captain of Poland's national team.
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Source: IAR, PAP, TVP Sport