The visitors, cheered on by a small contingent of 200 Iceland fans, took the lead after three minutes when Gylfi Sigurdsson beat keeper Wojciech Szczesny from the penalty spot to notch his 12th international goal.
Poland were roared on by a sellout crowd of 58,000 at the National Stadium but they lacked punch up front with Lewandowski, who scored 13 goals in Euro 2016 qualifying, being repeatedly caught offside.
The home team's best first-half opportunity came in the 31st minute when winger Kamil Grosicki's shot went just wide.
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Grosicki made amends eight minutes into the second half, scoring from just inside the area.
Poland went 2-1 up 14 minutes later when 18-year-old midfielder Bartosz Kapustka marked his second international appearance with his second goal.
Iceland struck back immediately as Alfred Finnbogason beat Szczesny but Lewandowski restored Poland's lead when he took advantage of chaos in the visiting defence following a corner.
Lewandowski, the Bundesliga's leading scorer this season with 14 goals, then made sure of victory in the 76th minute with an accurate drive from a narrow angle.
(Additional reporting by Jakub Iglewski; Writing by Wiktor Szary; Editing by Tony Jimenez)
