Thomas Müller followed his double against Norway in September with another two goals in Hamburg, with Toni Kroos also scoring.
It means that Germany top Group C on goal difference from Azerbaijan, ahead of their next game against Northern Ireland on Tuesday.
Boateng back for world champions
Germany made just one change from their 3-0 win against Norway last month, with Jérôme Boateng returning after injury in place of Benedikt Höwedes.
Ilkay Gündogan, back in the side after almost a year out, did not get a start but would appear in the second half.
The Czechs on the other hand made five changes from their goalless draw with Northern Ireland in their first group game, with the injured duo of Michal Kadlec and Vladimír Darida amongst those dropping out.
Karel Jarolím, in his third game in charge, gave starts instead to Tomáš Sivok, Jiří Skalák, Tomáš Hořava, Bořek Dočkal and Matěj Vydra.
Müller goal only reward for German dominance
The first half was utterly dominated by the home team, and although they took their time to get going, with Kroos’s wayward effort the only attempt in the first ten minutes, they would soon be in front.
And it was Müller was got his third goal in just the second game of qualifying. Mesut Özil set him up with a lay-off after a one-two with Mario Götze, and the Bayern Munich forward slotted it in with his first touch.
Their guests rarely got forward, despite showing some ambition at times, with Marek Suchý’s header wide from a free-kick the only thing resembling a shot.
And the Germans did have plenty of chances to get a second. Julian Draxler fired wide after Boateng’s long ball was picked up by Götze, whilst Müller had a shot tipped wide by Tomáš Vaclík, and Götze failed to get his dink over the keeper. And after good work from Götze, Müller couldn’t find the target as he shot over.
Kroos and Müller extend lead in second half
The Czechs barely even had a touch of the ball in the opening minutes of the second half, and inevitable Germany quickly had a second goal. Joshua Kimmich, in the midst of another impressive display, found Kroos, who perfectly placed his shot from outside the box.
They continued to dominate, with Özil having a shot put over with a deflection off Sivok. However Dočkal then gave Manuel Neuer something to do. His excellent strike was on target, with a reaction save from the goalkeeper to send it over instead.
And then Germany extended their lead yet further. It was well worked, with Özil and Jonas Hector combining on the left, with the left-back’s cross connecting with Müller who did the rest.
They would settle for three, despite Vaclík making saves from Müller, Kimmich and Höwedes. The Czechs had two more attempts on goal before stoppage, with Dočkal and Václav Kadlec going wide.
They perhaps should have scored with the final touch of the game, with Sivok firing in off the bar from a corner. The linesman though flagged for offside, although Sivok wasn’t the man in the offending position. The final whistle went straight after, so it would have only been a consolation after a thoroughly convincing display by the Germans.