The victory means Franciszek Smuda's side are undefeated this calendar year but they will surely face a sterner test on June 8 when they open the tournament against 2004 winners Greece.
In fact, one must question the benefit of playing a side that has only ever won three games in its entire history.
The gulf in class was obvious from the off and the hosts were never really stretched as they took a three goal lead to half-time with strikes from Ludovic Obraniak, Robert Lewandowski and a penalty from captain Jakub Błaszczykowski.
The raft of expected second-half substitutions dimmed the fluency of the game and the hosts only managed to add one further goal.
That came from the penalty spot when Marcin Wasilewski converted Poland’s second penalty of the game with a little over ten minutes remaining following a foul on Artur Sobiech.
Early Andorran intensity gave the game a competitive start but as soon as Maciej Rybus skipped by his man and found Obraniak to clinically dispatch past Josep Anton Gomez there was little doubt as to who would prevail.
Poland’s dominance should have been further rewarded before Lewandowski’s exquisite scissor kick doubled his side’s advantage but Błaszczykowski could not beat the Andorran keeper from close range after Lewandowski had charged down an attempted clearance and squared to his captain.
But Błaszczykowski was not to be denied and he added a third almost immediately after Lewandowski’s strike – having been felled in the box, he picked himself up and sent Gomez the wrong way from twelve yards.
With an expectant home crowd in full voice, more goals were expected at the Stadion Narodowy but they were not forthcoming as a host of substitutions turned the second-half into a more fractured affair.
A combination of courageous blocks and pretty solid goalkeeping kept the score down as the Poles began to lay siege to the visiting goal as the game drew to a close.
The home faithful were not to be denied another goal to cheer however as Wasilewski converted from the spot following a clear-cut foul on Sobiech by Andorran captain Ildefons Lima.