Sebastian Rudy and Sandro Wagner scored in the first half and Joshua Kimmich wrapped it up late as Germany made it nine wins from nine games to be certain of finishing top in Europe Group C.
Poland have 22 points from nine matches and need one more at home to Montenegro on Sunday to clinch their place in Russian Federation.
Martin Skrtel's own goal gave Scotland a 1-0 victory over 10-man Slovakia in Glasgow.
Poland will qualify for Russian Federation 2018 with a win if Montenegro versus Denmark ends in a draw, while three points will guarantee a play-off berth at a minimum.
Kamil Grosicki opened the scoring in the second minute and the visitors never looked back.
Robert Lewandowski scored a hat-trick to become Poland's leading goal scorer of all-time as his team thrashed Armenia 6-1 on Thursday night, leaving them on the verge of qualifying for 2018 World Cup Russia.
Hovhannes Hambardzumyan struck back for Armenia, who are already out of contention, but in the second half Jakub Blaszczykowski added another and Lewandowski netted his 50th global goal to seal his hat trick from close range.
Jakub Blaszczykowski and substitute Rafal Wolski also scored for Poland.
That means he now holds the all-time European record for most goals in a qualifying campaign - beating Cristiano Ronaldo's haul of 14, which the Portuguese superstar achieved as recently as August.
Christian Eriksen scored from the edge of the area 16 minutes into the game, a precious goal for Denmark to keep alive hope of automatic qualifying.
Constantin Budescu scored twice as Romania eased to a 3-1 win over Kazakhstan, with both teams already eliminated.
Germany picked up a 3-1 win over Northern Ireland at Windsor Park, securing their spot at next year's showpiece in Russian Federation.