The Germans took an early lead at the Eden Arena through Timo Werner, but the Czechs deservedly drew level when Hertha Berlin midfielder Vladimir Darida blasted home a superb equaliser with 12 minutes left.
However, Hummels rescued the world champions after a poor second half when his powerful header hit the net with just two minutes left.
“We had a lot of problems, the biggest one was giving away the ball too easily,” fumed match-winner Hummels.
“I haven’t seen a Germany team do that in the last 10 years.
“That wasn’t the football that we can — or want — to play.”
The win maintained Germany’s perfect run of seven straight wins on the road to Russia which leaves them five points clear of nearest rivals Northern Ireland in Group C with three games left.
Germany host fourth-placed Norway, who are out of the running, on Monday.
If Joachim Loew’s men win that and Northern Ireland fail to beat the Czechs, Germany will qualify before their trip to Belfast in October to face the Irish.
However, Germany’s head coach was far from impressed with what he saw in Prague.
– ‘lot of luck’ –
“We can’t be happy with the way we played,” said Loew.
“We had to have a lot of luck today and if Mat hadn’t scored with this great header, then we would have had to live with a draw.”
The defeat effectively ends the Czechs’ slim hopes of qualifying for the World Cup after collecting just nine points from their seven games so far.
Germany are now unbeaten in their past 30 World Cup qualifiers.
Their last defeat came exactly 16 years ago when they were hammered 5-1 by England in Munich as Michael Owen scored a hat-trick on September 1, 2001.
Loew started with six of the team which won the Confederations Cup final in July and four World Cup winners — Toni Kroos, Hummels, Mesut Ozil and Thomas Mueller.
Mueller, Germany’s captain for the night with Manuel Neuer just back from a fractured foot, was also highly critical.
“We simply made too many mistakes,” said the Bayern Munich star.
“In our build up play, we often served the ball up to the Czechs and made life hard for ourselves.”
With just four minutes gone, the Germans grabbed the lead after pressing the Czech defence around their own box.
Centre-back Hummels intercepted a stray pass inside his half and his pass found Ozil, who put the ball in behind the defence, allowing Werner to turn and tuck his shot past Czech goalkeeper Tomas Vaclik.
Lars Stindl went close with a chance in the first half, but the hosts threatened the Germans with a plucky display.
Michael Krmencik fired over after trying to lob Barcelona goalkeeper Marc-Andre ter Stegen in the German goal.
Defender Theodor Gebre Selassie, who plies his trader in Germany for Werder Bremen, also went close for the hosts.
The Czechs were clearly the best team in the second half.
Tomas Soucek tested Ter Stegen, while Germany’s forwards, led by Arsenal’s attacking midfielder Ozil, struggled to put together telling attacks.
The equaliser was worth the wait as Darida hit the top right-hand corner from 25 yards out, rifling an unstoppable effort past Ter Stegen.
But the Germans secured the three points when Kroos floated a free-kick to Hummels, whose bullet header flew past Vaclik.
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