The Sochaux defender headed in the only goal of the game, his first international goal, as Smuda's men wrapped up another warmup victory.
Damien Perquis headed in the only goal of the game on the half-hour, though Maciej Rybus should have made it two after hitting the post just before halftime.
Coach Franciszek Smuda opted to change much of the side that secured a narrow 1-0 success against Latvia on Tuesday, with only four players retaining starting berths. In came Arsenal goalkeeper Wojciech Szczesny, as well as Borussia Dortmund trio Lukas Piszczek, Robert Lewandowski and Jakub Blaszczykowski with Napoli's Marek Hamsik starting for the visitors.
Poland took a well-deserved lead on the half-hour. A fine delivery from Piszczek saw Perquis rise highest to head the ball past Pernis and into the back of the net. It would also mark the Sochaux defender's first international goal.
The White Eagles dominated after, and should have doubled their lead before the break. The effective Maciej Rybus waltzed into the box after a neat ball played by Rafal Murawski, but the Terek Grozny midfielder's strike slammed into the post instead as Poland held a 1-0 halftime lead.
The second half would be an all too different affair, with the number of substitutions changing the familiarity of the game, though Poland spurned another decent opportunity. Dariusz Dudka, on for Murawski headed narrowly over the bar from Obraniak's corner.
Slovakia was noticeably better after the break, but failed to negotiate a way past Szczesny. Hamsik proved unsuccessful with a tame strike, before substitute Marek Bokos' effort was saved by the Arsenal goalkeeper.
Poland, which was devoid of any attacking creativity with the departures of Lewandowski and Blaszczykowski in the second period, with Marek Cech also firing in a low shot from the edge of the box, as Smuda's men hung on to claim the win.
The Euro 2012 host now faces Andorra in its final warmup match on June 2, before kicking off this summer's show-piece with the opening game against Greece in Warsaw on June 8.
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