Zheng swapped a pair of breaks with her 19th-seeded opponent in the opening set and fought back from 4-2 down in the tiebreak to get her nose in front before allowing big-hitting Samsonova to hold in a tense first game of the second set.
The Russian broke to love in the next game and struck again later to draw level in the match, leaving Zheng with a big fight on her hands to reach her maiden Roland Garros quarter-final at the site of her Paris Games triumph last year.
Zheng showed the mettle of a gold medallist, however, as the 22-year-old broke for a 4-2 lead and shrugged off a poor service game to get ahead 5-3 before securing victory when Samsonova made an unforced error.
"Right now I feel incredible because I've been dreaming of reaching this stage, it did not happen in 2023 and 2024. I have no words to describe my emotions right now," said Zheng, who dropped to the ground in celebration.
"The crowd helped me a lot, they gave me a lot of energy. I like to play in front of a lot of people. It gives me a lot of motivation. I hope I can stay longer in Roland Garros.
"It was an intense match. She put me under a lot of pressure and I ran a lot behind the baseline. But I have a lot of energy. I can play five sets if needed. My body is feeling great and I will push till the end."
Zheng takes on either world number one Aryna Sabalenka or Amanda Anisimova in the next round.