The result left the Poles in charge midway through the campaign on 13 points from five games, six ahead of closest rivals Montenegro and Denmark, who were held 0-0 in Romania.
Lewandowski curled home a superb 40th-minute free kick and, although Stefan Mugosa equalised just past the hour, Piszczek got the winner with a fine lob in the 82nd after the Poles missed a barrage of chances against their injury-hit opponents.
The visitors had come close three times in the opening half before Lewandowski netted his eighth goal of the qualifying campaign, leaving goalkeeper Mladen Bozovic rooted to his line with a delightful strike from 25 metres.
Lewandowski and Piszczek missed a pair of easy chances inside a minute on the hour and Poland were swiftly punished as Mugosa scored his first international goal with a thumping header after Damir Kojasevic's teasing cross from the right.
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Poland pressed for a winner and right back Piszczek made amends for his earlier miss as he brilliantly side-footed the ball over Bozovic from inside the penalty area to silence a vociferous home crowd in the Adriatic nation's capital.
(Writing by Zoran Milosavljevic in Belgrade; Editing by Ken Ferris)
