As the fifth seed, Garcia is by a distance the top-ranked French player in either the men’s or women’s singles but the country’s wait for a new grand slam champion goes on.
Blinkova, ranked 56, had never beaten a top-five player before but battled back from a set down to triumph 4-6 6-3 7-5, finally taking her ninth match point.
Nerves were clearly affecting the 24-year-old, who served for the match twice, while the partisan Philippe Chatrier crowd were willing Garcia on, but Blinkova did not let the opportunity for the biggest win of her life slip away.
Former world number three Elina Svitolina continued to impress in her comeback grand slam, taking inspiration from husband Gael Monfils as she saw off Australian Storm Hunter 3-6 6-3 6-1.
Less than 11 hours after completing an emotional five-set win over Sebastian Baez, Monfils was back at Roland Garros cheering on Svitolina.
“I watched him, but not live, I was screaming in my room,” said the Ukrainian. “It was an unbelievable match. I don’t know what he is doing here now, I think he should be resting, but I’m really thankful for him coming to support me, especially in this tough match.”
Svitolina is playing her first slam in more than a year following the birth of baby Skai last October.
The new mother and father are juggling the day job with childcare, and Svitolina said: “It’s the first tournament for us where we are both playing at the same tournament, and Skai is here with us in Paris as well. It’s really, really special.
“So far everything is going well and we really enjoy our time off the court together and on the court we try to be focused and play as good as we can.”
Svitolina is also having to put to one side thoughts of the troubles in her homeland and is using the situation to inspire her on court.
She said: “When I step on the court, I just try to think about the fighting spirit that all of us Ukrainians have and how Ukrainians are fighting for their values, for their freedom in Ukraine. And me, I’m fighting here on my own frontline.
“I cannot be sad. I cannot be distracted in some ways. I’m just going to lose. I have a flag next to my name so I’m fighting for my country, and I’m going to do that each time I step on the court.”
Third seed Jessica Pegula had an untaxing afternoon, taking the first set 6-2 against Camila Giorgi before the Italian pulled out.
Ninth seed Daria Kasatkina produced the shot of the tournament so far, a fizzing tweener winner, in a 6-3 6-4 victory over former finalist Marketa Vondrousova, while 2017 champion Jelena Ostapenko lost out 6-3 1-6 6-2 to American Peyton Stearns.
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