Poland were leading 1-0 when Lewandowski added their second in the 89th minute, before he grabbed two more in stoppage time to put Poland a provisional three points clear at the top of the group.
The win moves Poland closer to a third Euros helped by their shock 2-0 victory over group favourites Germany in October.
They have 14 points from six games ahead of Scotland, who have 11 after a 1-1 draw in Ireland, and Germany, who were playing away at Gibraltar later on Saturday, with 10 points.
"There's no way anyone among us would be afraid of being a
front-runner," said Poland coach Adam Nawalka.
Georgia manager Kakhaber Tskhadadze added: "Poland were like a machine (tonight) and this team can achieve a lot."
The 57,000 fans at the National Stadium had to wait more than an hour for the first goal with Lewandowski wasting two perfect chances to open the scoring while his team mates also struggled to break through Georgia's five-man defence line.
The opener came after 62 minutes when Lewandowski's 21-year-old strike partner Arkadiusz Milik fired home from 20-metres with a beautiful strike after a corner.
Georgia came close to an equaliser when full back Georgi Navalovsky's powerful shot hit the bar minutes before Lewandowski came to life with his quick-fire treble.
The Bayern Munich striker, who had suffered a frustrating night in front of goal, capitalised on two clever passes from Milik and one from his former Borussia Dortmund team mate Jakub Blaszczykowski to wrap up the points for the hosts.
"It was definitely the first time I've scored so many in such a short time," Lewandowski said.
Turkey's Arif Erdem scored the fastest European Championship qualifying hat-trick in three minutes against Northern Ireland in the Euro 2000 campaign according to Infostrada Sports.
(Editing by Ken Ferris and Toby Davis)
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