The hosts took the lead with just 12 minutes on the clock when Alan Hutton gifted the ball to Krzysztof Maczynski on the edge of the box, allowing the midfielder to pass an accurate effort in off the post.
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Scotland responded well to that setback, however, and were back level just six minutes later as James Morrison and Ikechi Anya combined to set up Shaun Maloney, who guided a calm finish past Wojciech Szczesny from inside the box.
The game continued to be played at a good pace, and Poland almost regained their one-goal advantage shortly before the half-hour mark when Arkadiusz Milik found himself in space, but his shot was easy for David Marshall.
The visitors had an opening of their own a little less than 10 minutes before the break when Steven Fletcher made room to shoot from the edge of the box, but he dragged his shot wide as the teams went into half time all square.