Zheng is the second Chinese player to reach the singles semi-finals at an Olympics after Li Na, who finished fourth at the Beijing 2008 Games.
After two tough sets, Kerber, who won a silver medal at Rio 2016, took the lead in the third to 4-1 and received a standing ovation from an enthusiastic French crowd after saving a huge break point.
Having run out of steam on a hot and humid Philippe Chatrier court and lost 10 points in a row, she bounced back to 4-4. But the Zhen's powerful shots allowed her to win the tie-break.
Reaching the quarter-finals, at a tournament she had said would be her last, was the former world number one's best performance this year after returning from maternity leave in January.
"I've achieved everything I dreamt of," the three-time Grand Slam champion said. "I was number one, won Grand Slams, won a (silver) medal in Rio, so what more could you want in the end?"
The German had lost in the first round of this year's three Grand Slams so far, the Australian and French Open followed by Wimbledon.
Zheng reached a career-high ranking of seven after her runner-up finish at the Australian Open.
