In Klagenfurt, where they will also face Slovakia on Saturday in another pre-EURO friendly, the Poland largely dominated their Baltic opponents.
But despite a decent set of performances, notably Celtic striker Pawel Brozek and midfielders Adrian Mierzejewski of Trabzonspor and Rafal Murawski of Lech Poznan, they only made their mark in the final minutes when Artur Sobiech celebrated his first apperance since 2010 with the only goal.
That will give some cause for concern when they start the tournament proper with resilient opponents Greece, the Czech Republic and Russia in their group. Poland manager Franciszek Smuda was nonetheless upbeat. "Some say that the result's not what it's about, and that simply playing is the key thing. But the lads won, and that matters," he said.
With Poland midway through a training camp in Austria, Smuda opted to rest the big names who have just wrapped up their club seasons, notably his Borussia Dortmund trio of striker Robert Lewandowski, midfielder Kuba Blaszczykowski and defender Lukasz Piszczek.
Arsenal goalkeeper Wojciech Szczesny was also stood down allowing his understudy at club and national level Lukasz Fabianski to show his mettle. Attacks were few and far between in the first half, though, Polish teenager Rafael Wolski took the eye on his debut.
Poland did at last get the ball in the net in the 55th minute through Werder Bremen defender Sebastian Boenisch, who latched onto a free-kick from Sivaspor midfielder Kamil Grosicki, however, it was ruled out for offside.
Grosicki was to find his creative work rewarded less than ten minutes from time, though, as his pass was hit guided the net by Hannover 96 forward Sobiech. "This was a great result for the whole team," Sobiech said. "I'm the joker in the pack at my club too!"
Klagenfurt brings back bad memories for Poland fans who recall their poor EURO debut in 2008. Having failed to reach the 2010 FIFA World Cup™, and with an automatic hosts' berth at EURO 2012, Poland will have gone 968 days without a competitive match by the time they kick off the tournament, hosted with neighbouring Ukraine, on 8 June in Warsaw.