Michal Sadilek gave the Czechs an early lead in the sixth minute, converting smartly after Adam HloΕΎek's cross from the right was touched on by Alexandr Sojka.
It was the earliest goal scored at this World Cup and gave Czechia a platform they looked in control of for most of the first hour.
Patrik Schick, their most dangerous attacker, wasted the best chances to extend the lead, heading over from close range before the break and failing to convert another headed opportunity early in the second half.
South Africa, who lost their opener to Mexico, had offered little in attack and looked destined for a second defeat when Pavel Sulc's arm diverted Thapelo Maseko's goal-bound shot inside the penalty area in the 81st minute. VAR confirmed the handball, and Mokoena stepped up to send the goalkeeper the wrong way.
Head coach Hugo Broos was proud of the character his team showed but honest about what lay ahead.
"I'm very proud of my team. This is Bafana Bafana β we love good football, we are aggressive, we create chances. Yes, we made mistakes, but I'm very proud of the performance today," Broos said.
"The Czechia team is powerful and very tall. We did very well. It's a little bit of a pity that it's only 1-1, but we just have to win the game against Korea Republic, which will be very difficult too.
"If we play with the same mentality, it will be possible."
Both sides now have one point from two matches, leaving them in a difficult position going into the final round. South Africa face South Korea next, while Czechia play Mexico β both formidable opponents with something to play for.
Czechia will rue Schick's wastefulness above all. Had he taken either of his headed chances, the group picture would look very different. Instead, they must win their final match to have any realistic hope of reaching the last 32.
The match was also notable for being officiated entirely by a female crew, led by referee Tori Penso.