Stephens ousted in Hobart, Ostapenko overcomes Cirstea in Adelaide
The duo slugged it out for nearly three hours before the Chinese world number 73 clinched the third set tie-break for a memorable victory.
Having split the first two sets, Yuan broke Stephens when the American was serving for the match at 6-5. Stephens led 5-4 in the tie-break but could not hold on to her advantage and crashed out.
"I'm very happy and excited to win," a beaming Yuan.
"She's a Grand Slam champion. At home, I'd (often) watch her play on the TV. I'm happy to be here (playing against her)," she said of her opponent.
Former Australian Open champion Sofia Kenin began her campaign at the Melbourne Park warm-up event with a 6-3, 6-3 win against Greet Minnen of Belgium.
Kenin, who saved all three break points she faced in the match, will meet Daria Saville for a spot in the quarter-finals.
In the first round of the Adelaide International, sixth seed Jelena Ostapenko came back from a sluggish start to beat Sorana Cirstea 2-6, 6-2, 6-4.
Ostapenko, a quarter-finalist at last week's Brisbane International, needed nearly two hours to settle the match at the Australian Open tune-up event, enjoying a modicum of revenge after the Romanian beat her at Wimbledon last year.
Cirstea won four games in a row to race through the opening set but former French Open champion Ostapenko hit back in the second and fired back-to-back aces to force the decider.
The Latvian then raced to a 5-2 lead but was broken serving for the match. She blew two match points at 5-3 but went on to seal victory with her sixth ace.
Laura Siegemund, who was part of the Germany team that won the United Cup title last week, upset world number 14 Liudmila Samsonova 6-7(1), 6-4, 6-4.
Elsewhere, returning to the tour for the first time since last year's Wimbledon, Denis Shapovalov lost 6-4, 6-2 to Sebastian Ofner at Auckland Classic.