A packed 56,000 crowd at the National Stadium in Warsaw saw the home team go in front in the 20th minute when Kamil Grosicki delivered a cross and Lewandowski scored from close range.
Poland kept attacking, mainly down the wings, and Lewandowski made it 2-0 with a penalty nine minutes before halftime.
Full back Jannik Vestergaard brought down Arek Milik six metres out and Lewandowski sent keeper Kasper Schmeichel the wrong way from the spot.
The Bayern Munich marksman's third goal came at the start of the second half when he pounced on an error by Vestergaard and powered half the length of the field before slotting the ball beyond Schmeichel.
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Denmark pulled one back in the 49th minute as Poland's Kamil Glik turned the ball past his own keeper, Lukasz Fabianski.
The visitors then suddenly started to dominate possession and it was no surprise when lively substitute Yussuf Poulsen netted in the 69th minute.
However, with playmaker Christian Eriksen tightly marked by Poland's defenders, Denmark were unable to draw level.
Poland are joint top of the group, alongside Montenegro and Romania, with four points from two matches. The Danes are fourth on three points.
Lewandowski has now scored hat-tricks in three competitions this season, having also landed a treble in the Bundesliga and German Cup.
He has netted in each of his last seven World Cup/European Championship qualifiers, bagging 11 goals in total in those matches.
(Reporting by Jakub Iglewski; Editing by Tony Jimenez)
