The Poles will lean heavily on their Borussia Dortmund trio - striker Robert Lewandowski, captain Jakub Blaszczykowski and defender Lukasz Piszczek - in the Euros and all three started against Andorra.
Ludovic Obraniak opened the scoring in the 13th minute and Lewandowski made it 2-0 nine minutes before half-time.
Poland, who have now gone five matches without conceding a goal, added a third through Blaszczykowski before Marcin Wasilewski completed the rout with a 77th-minute penalty.
"I'm pleased with the result and that all the players are okay," said coach Franciszek Smuda.
The Poles have had little to celebrate in recent years but hopes are high among the fans that Smuda's team can advance beyond the group stage where they will meet Russia, Czech Republic and Greece.
The Euros, co-hosted by Ukraine, begin on Friday.
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