Teboho Mokoena slotted home the late spotkick which gave South Africa a lifeline as they were staring at potential early elimination, after the Czechs had led from the sixth minute through Michal Sadilek.
Both teams now have a point after losing their respective opening games last Thursday. Mexico and South Korea, both on three points, meet in Guadalajara later on Thursday.
For the first time at a World Cup match, both head coaches were aged over 70, and the two 74-year-old managers opted to shake things up after their sides put in poor performances in their opening-game defeats.
South Africa's manager Hugo Broos ditched his much-criticised conservative formation, while Czech boss Miroslav Koubek made five changes to his team.
Patrik Schick completely mishit a header in the opening minute as the Czechs began on the front foot and found the early goal when the South African defence was caught napping on a long throw-in.