Mladenovic won all three points for her team, defeating Ajla Tomljanovic on the first day and then getting a three-set win against No. 1 Ashleigh Barty before partnering with Caroline Garcia to a win in the deciding doubles.
The win against Barty in front of a packed Aussie crowd was particularly memorable for the Frenchwoman.
"I took it like a Grand Slam final," said Mladenovic. "When I beat her in Rome just before she won Roland Garros, it was special. But when I beat Ashleigh Barty in Rome, there were not 15,000 people. She wasn't No. 1.
"The level we played was exceptional... [Winning] 7-6 against Ash Barty in front of such a crowd, it's one of the biggest moments of my career."
Calling her performance "unbelievable," Mladenovic said, "I'm giving it to the people behind the scenes, the team and the girls who were supporting from first to final point."
Thiem, who is playing this week's ATP Finals in London, woke up to hear about Mladenovic's heroics. The Austrian sent congratulations to his girlfriend before playing his opening round robin in the evening.
"I didn’t watch it," he told press at London. "I couldn’t disrupt my preparations. But she won three points in the match, beating the world No. 1, and probably it’s something very few players have done. I am super happy for her."
Thiem followed suit with a straight-sets win against Roger Federer, declaring himself at the start of the elite eight event.
The No.5 was also happy to win against the No. 3 and six-time champion. "He is an absolute legend," he said.
Thiem next plays Novak Djokovic on Tuesday in London.