Blaszczykowski, who is on loan at Fiorentina, found space in the area and scored in the 28th minute with a seemingly-effortless first-time shot after Serbia had failed to clear their lines.
The 30-year-old winger has recently fallen out of favour at the Italian club, but improved his chances of earning a place at the Euros in June and July with a performance that overshadowed his more heralded team mates Robert Lewandowski and Arek Milik.
Playing on a rain-soaked pitch in the western Polish town of Poznan, the hosts struggled on the flanks against Serbia's experienced full backs Aleksandar Kolarov and Branislav Ivanovic.
Poland coach Adam Nawalka fielded a largely full-strength side that featured Sevilla midfielder Grzegorz Krychowiak and Torino defender Kamil Glik, but Serbia managed to keep them at bay for most of the game.
It was a physical encounter as Serbia fought tenaciously in midfield, with Lewandowski almost forced off the pitch through injury following a tackle early in the game.
Poland are in Group C at Euro 2016 along with world champions Germany, Ukraine and Northern Ireland.
(Editing by Toby Davis)
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