The world number one has been living up to her billing since the turn of the year and took less than an hour to see off her fellow American.
A break in the opening game of the first set sent Williams on her way to the lead, losing just six points on her own serve.
Stephens' service game evaded her for the entirety of the second set, losing all three to Williams, only really putting up a fight as she squandered two break points at 3-0 down.
Svetlana Kuznetsova will meet Sam Stosur in the third round following a hard-fought 6-3 5-7 7-5 win against Garbine Muguruza.
Stosur was a 6-3 6-2 victor over Kaia Kanepi, and Roberta Vinci defeated Alize Cornet 6-4 7-5.
Caroline Wozniacki overcame an early scare to race to a 7-5 6-0 Christina McHale.
The Danish fifth seed was broken in the first game and, despite resorting parity at 2-2, she dropped serve immediately as McHale showed early promise.
However, a mammoth eighth game that lasted 24 points saw the American's resolve - and serve - broken and she failed on serve again at 5-6 to lose the set, with Wozniacki dominant in the second.
Wozniacki will now face Agnieszka Radwanska, who saw off Casey Dellacqua in her second-round clash, cruising to a 6-2 6-1 triumph against the Australian.
Having won the opening three games, Radwanska required five set points to move in front with a second break of serve in the eighth.
The second set was largely a precession, with Dellacqua managing to get just a single game on the board, sandwiched between two three-game streaks for Radwanska.
Meanwhile, 13th seed Lucie Safarova beat Tsvetana Pironkova 6-3 6-1, and Andrea Petkovic was forced to withdraw from the tournament due to a "gastrointestinal illness", sending Irina-Camelia Begu into the third round.