Lewandowski, who is 33/1 with Sky Bet to win the Golden Boot award at this year's World Cup, broke the deadlock in the 19th minute when he curled in a cut-back from Maciej Rybus in Warsaw.
The wantaway Bayern striker doubled the hosts' lead just after the half-hour mark when his 20-yard free-kick went in off the underside of the crossbar.
Following a string of second-half substitutions, including Juventus goalkeeper Wojciech Szczesny coming on for Swansea's Lukasz Fabianski, Poland thought they had further extended their lead.
Grzegorz Krychowiak flicked in a backheel following a corner - but the West Brom midfielder saw his effort disallowed on review for a handball.
It was 3-0 in the 71st minute when Sampdoria forward Dawid Kownacki tapped home from close range after being set up by Bartosz Bereszynski.
Wolfsburg midfielder Jakub Blaszczykowski wrapped up a comfortable win via the penalty spot eight minutes from full-time.
Poland open their Group H campaign against Senegal in Moscow on June 19, before fixtures against Colombia and Japan.
The Samurai Blue, meanwhile, had earlier beaten Paraguay 4-2 in Innsbruck ahead of their departure to Russia.
