Timo Werner gave Germany a flying start when he scored his fourth goal in his last four internationals early on, but Vladimir Darida earned the Czechs a deserved equaliser with a thumping long-range drive in the 78th minute.
Hummels, however, floored the hosts with his goal which left Germany on 21 points at the top of European Group C, five clear of Northern Ireland who won 3-0 in San Marino.
Despite a valiant display, the Czechs are a further seven points behind in third and almost out of the running for a second-place finish. Their last throw of the dice will be on Monday when they visit the Irish.
Germany could qualify for the World Cup on the same day if they beat Norway at home and the Irish fail to beat the Czechs.
The group winners qualify directly for Russia while the eight best second-placed teams in the nine groups go into a playoff round.
"Of course, we cannot be satisfied with the way we played," said Germany coach Joachim Loew. "The Czech Republic defended well, but we made life difficult for ourselves."
There was a disappointingly large number of empty seats as the game got under way in a lukewarm atmosphere and the Germans were quick to put a further dampener on the hosts' evening.
The Czechs lost possession early on and Mesut Ozil slipped the ball to Werner who controlled it impeccably and fired his shot past Tomas Vaclik.
The home side then came to life and Jan Kopic had an effort blocked by Lars Stindl before Jan Boril burst forward and tested Marc-Andre ter Stegen with a low drive which the goalkeeper turned around the post.
Michael Krmencik then tried to cunningly lob Ter Stegen but his effort was just over the bar.
In between, Germany nearly scored a second when Stindl was foiled by Vaclik at the end of a flowing move.
The Czechs continued to press forward in the second half and were finally rewarded in the 78th minute when a throw-in on the left was worked to Darida who let fly with a rising shot which flew into the top corner.
The Germans had a final sting in the tail, however, when they won a free kick in midfield and Toni Kroos floated a pinpoint ball towards Hummels who sent an unstoppable header into the top corner.
Norway beat Azerbaijan 2-0 with a penalty from Joshua King and an own goal from Rashad Farhad Sadygov in the group's other match, leaving both teams on seven points and out of the running for second place.
San Marino are bottom after losing all their games.
(Writing by Brian Homewood, editing by Ed Osmond and Christian Radnedge)
