Seventh-ranked Zheng triumphed 6-2, 7-5 and will face either Croatia's Donna Vekic or Anna Karolina Schmiedlova of Slovakia in the gold medal match.
"I feel more than just happy -- happy isn't enough to describe how I feel," said Zheng, who had played back-to-back three-hour matches to make the semi-final.
"If you ask me to play another three hours for my country, I would. It was an amazing match. To beat Iga is not easy as it's an important event for her."
Swiatek, a four-time French Open champion at Roland Garros, went into the match at a sweltering Court Philippe Chatrier having not lost in Paris since 2021.
The 23-year-old had also defeated Zheng in all of their six previous meetings.
However, she was hit off the court by the powerful 21-year-old Australian Open finalist who broke the Pole three times in the opening set.
Swiatek appeared restored by a 10-minute break and quickly stretched out to 4-0 lead in the second set before Zheng battled back, retrieving both breaks for 4-4.
The Chinese star broke again for a 6-5 lead against the error-plagued Swiatek and claimed victory in the next game.
By making the final, Zheng is the first Chinese man or woman to reach an Olympic singles gold medal match, bettering the run of Li Na who finished fourth in the women's event at Beijing in 2008.
Djokovic, still seeking an elusive Olympic gold medal, takes on Stefanos Tsitsipas on the same Court Philippe Chatrier where in 2021 he battled back from two sets to defeat the Greek in the French Open final.
Top seed Djokovic has coasted through the first three rounds in Paris and will be buoyed by his 11-2 head-to-head record over Tsitsipas.
That run also included victory in the final of the 2023 Australian Open final while Tsitsipas's last win over the Serb came back in 2019.
Alcaraz, back at Roland Garros where he won a maiden French Open in June, can become the youngest Olympic semi-finalist since Djokovic in 2008.
Murray finale?
The 21-year-old Spaniard, who successfully defended his Wimbledon title last month, faces Tommy Paul of the United States.
Paul will return to the courts later Thursday when he teams up with Taylor Fritz in a men's doubles quarter-final which could mark the end of Andy Murray's career.
Murray and Dan Evans will face the US third seeds for a place in the semi-finals.
Murray, a former world number one and three-time Grand Slam singles champion, has already announced his intention to retire after the Olympics.
He and Evans have endured a roller-coaster Olympics so far, saving seven match points over two rounds.
"I don't think he wants to go home," said Evans of his 37-year-old teammate.
In the day's other men's singles quarter-finals, third seeded and defending champion Alexander Zverev of Germany takes on 11th-seeded Lorenzo Musetti of Italy.
Former two-time French Open runner-up Casper Ruud, seeded six of Norway, meets 13th seeded Felix Auger-Aliassime of Canada.
Aliassime made the quarter-finals by knocking out fourth seed Daniil Medvedev, the Russian appearing as a neutral in Paris, in the last 16.
