After Patrik Schick headed an early chance wide at the far post, the Czechs – showing five changes from the 2-1 defeat to South Korea, including midfielder Tomas Soucek dropped to the bench – took the lead in the sixth minute on Thursday (Friday AEST).
Adam Hlozek raced on to a throw-in down the right and cut the ball back to the edge of box where Alexandr Sojka fed Michal Sadilek to clip his finish past South Africa keeper Ronwen Williams for the quickest goal of the tournament so far.
South Africa, who had Yaya Sithole and Themba Zwane sent off in their opening 2-0 loss to co-hosts Mexico at the Azteca Stadium, looked for a response as Oswin Appollis' 25-yard effort was deflected behind.
That came just before the first hydration break, which was again met by a chorus of boos from fans at the Mercedes-Benz Stadium, where the roof was closed.
The tempo dropped heading towards halftime before Thapelo Maseko was played into the right side of the Czech penalty area, but his angled effort was cut out at the near post.
South Africa sent on Orlando Pirates forward Relebohile Mofokeng for the second half, but it was the Czechs who nearly struck when Vladimir Darida saw his close-range shot blocked before Lukas Cerv's speculative effort was tipped over.
From the resulting corner, Bayer Leverkusen front man Schick then headed straight at Williams
South Africa were awarded a penalty with nine minutes left for handball by Czech substitute Pavel Sulc, having been struck at point-blank range from a shot by Maseko.
Mokoena made no mistake from the spot, slotting the ball to the left and sending Matej Kovar the wrong way.
Neither side was able to find a late winner – Evidence Makgopa shooting straight at Kovar after a strong turn on the edge of the box – which leaves both countries still with some hope of making the last 32.
The Czech Republic face Mexico at the Azteca in their final group game while South Africa take on South Korea in Monterrey.
South Africa coach Hugo Broos felt "very proud" of his team. "When you see the reaction after our game against Mexico, this is Bafana Bafana," he said in his pitchside interview.
"We play good football, we are aggressive, we had chances, but you need also a little bit of luck.
"Now we don't have to count on someone else. We just have to win the game against South Korea, which will be very difficult too, but when we play with the same mentality I think it is possible."
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