In the first two sets, Thiem clinched 18 winners, committed just four unforced errors and broke serve four times on seven occasions.
Speaking on court, she said: "It was intense". It brings out the best in my fitness when I play Sloane.
Serena's three-year-old daughter was busy playing with toys for most of her mom's match.
This was a rematch from less than two weeks ago at the Western & Southern Open.
In the round 3 game, Williams, 38, eliminated Stephens 2-1 with the sets of 2-6, 6-2 and 6-2 to march to the next phase, where she will face Greek player Maria Sakkari. She'll take on the victor of Alizé Cornet and Tsvetana Pironkova in the next round.
However, the doubts that have crept into Williams' formidable psyche resurfaced with two errors that gave Sakkari the set.
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But it was clear to anyone watching that 3-year-old Olympia was very much enjoying watching her mama play. Williams struggled with her pace, and her movement, and it meant trouble very quickly, as Stephens broke her in Game 3 of the first, Williams yanking a forehand wide to close it, then went up 3-1 with a gorgeous crosscourt forehand victor.
She sent down a dozen aces including one on her second serve.
"I'm so moved by the outpouring of support behind my story about Kobe", Duncan said in response to the hashtag trending. "Otherwise there is no chance against her".
Williams looked tense from the start and Stephens exploited that to the full with intelligent placement and a crispness of shot that made her opponent look slow.
And third seed Daniil Medvedev appears against American wildcard J.J. Wolf in a last-32 match.
The end of the first set was met by total silence - not even the awkward, manufactured soundtrack piped in during other matches to simulate ambient noise. She was just playing so clean and I just said: "I don't want to lose in straight sets". "We all hope she gets to it, " Stephens said.