The top-ranked Williams broke Stephens four times and saved both break points she faced to secure her 25th straight win. She will next face the winner between Victoria Azarenka and Ajla Tomljanovic.
"She's such a tough player," Williams said of Stephens. "I've never won a 6-0 set against her before, and I don't think I can ever do that again."
Williams remained undefeated in 2015, with her last loss coming in round-robin play at last year's WTA finals.
Earlier, Caroline Wozniacki powered past Christina McHale of the United States 7-5, 6-0 Monday to reach the third round of the Madrid Open.
The fifth-seeded Wozniacki hit five aces and committed fewer unforced errors on the red clay to beat the 22-year-old player from Teaneck, New Jersey in 1 hour, 30 minutes. Wozniacki will face Agnieszka Radwanska after the Polish player eased past Casey Dellacqua of Australia 6-2, 6-1.
In the men's competition, John Isner of the United States beat Adrian Mannarino of France 7-6 (2), 6-4 to reach the second round.
The 16th-seeded Isner will next play either Jeremy Chardy - another Frenchman - or Thomaz Bellucci of Brazil.
Also, Steve Johnson of the United States came from a set down to beat Alejandro Gonzalez of Colombia 4-6, 6-3, 7-6 (4).
The 25-year-old Johnson from Redondo Beach, California - one of five Americans in the men's main draw in Madrid - will now have a day to recover before facing third-seeded Rafael Nadal of Spain in the second round.
Sam Querrey beat 19-year-old qualifier Thanasi Kokkinakis of Australia 6-4, 6-7 (6), 6-3 - hitting 11 aces in the process, while Feliciano Lopez of Spain overcame Benjamin Becker of Germany 7-5, 3-6, 6-4.
The 11th-seeded Lopez, who lives in Madrid, was given a warning by the chair umpire for using foul language on court during a tense third set.
Marin Cilic of Croatia seeded ninth beat Jiri Vesely of the Czech Republic 7-5, 6-1 and David Goffin of Belgium rallied to defeat Ernests Gulbis of Latvia 3-6, 6-1, 7-5.
Joao Sousa of Portugal beat Jerzy Janowicz of Poland 6-4, 7-5 and Fabio Fognini of Italy defeated Santiago Giraldo of Colombia 6-2, 6-3.
In the women's tournament, 13th-seeded Lucie Safarova of the Czech Republic bested Tsvetana Pironkova of Bulgaria 6-3, 6-1, Samantha Stosur of Australia beat Kaia Kanepi of Estonia 6-3, 6-2, and 21-year-old Garbine Muguruza of Spain lost to Svetlana Juznetsova of Russia 6-3, 5-7, 7-5.
Roberta Vinci of Italy beat Alize Cornet of France 6-4, 7-5.