The Poles are now second in Group D on 17 points, two behind leaders Germany with two matches remaining.
Ireland are third on 15 points with Scotland fourth on 11. The top two progress to next year's finals in France.
"It all depends on us and if we play as well as we have so far we shouldn't be afraid," said Milik of the final games against Scotland and Ireland.
"Second position is good and we just need to do everything possible to qualify and not let such an opportunity go."
Grosicki struck twice in the opening 15 minutes before another quickfire double from Lewandowski put the Poles 4-0 up by halftime.
Milik was on target twice in the second half while Jakub Blaszczykowski added a penalty and Bartosz Kapustka also netted.
Gibraltar, UEFA's newest international team, fielded just one professional player -- Jake Gosling of Bristol Rovers -- and he scored a consolation goal in the 87th minute.
It was only their second goal in the qualifying campaign but it did little to lift their spirits as they stayed rooted to the foot of the table with zero points from eight games.
"We are obviously very disappointed," said coach Jeff Wood after his Gibraltar team were on the receiving end of another hiding following Friday's 4-0 qualifying defeat by Ireland.
"I don't want to make any excuses but hardly any of the players have played competitive games since May and we weren't ready."
(Reporting by Jakub Iglewski,; Editing by Tony Jimenez)
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