Williams, playing her third match at Indian Wells after deciding to end a 14-year boycott of the event where she had suffered alleged racist abuse, enjoyed plenty of support but struggled early to find her form.
Top seed Serena Williams overcame a wobbly start to see off a determined Sloane Stephens 6-7 (3) 6-2 6-2 on Tuesday and advance to the quarter-finals of the BNP Paribas Open.
Williams, playing her third match at Indian Wells after deciding to end a 14-year boycott of the event, where she had suffered alleged racist abuse, enjoyed plenty of support but struggled early to find form.
Stephens, who reached the quarter-finals a year ago, looked ready to return to the last eight after breaking Williams twice, but in the end there was no denying Williams as she extended her winning run to 14 matches.
Indian Wells Open: Serena Williams breezes into fourth round
On another sun-bathed afternoon Stephens got the contest off to a bright start charging in front 3-0. But Williams, who has not lost since last year's WTA Finals in Singapore, quickly got her game in gear sweeping through the next four games before her opponent could again hold serve.
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Displaying plenty of grit of her own, Stephens dug in to force the opening set to a tiebreak that she dominated.Playing with a greater urgency, Williams broke Stephens twice to open the second and go up 5-2 before serving out the set to level the match.
The third set followed a similar script as Williams, playing her first event since winning her 19th grand slam title, and sixth at the Australian Open, recorded the early break to secure a 2-0 advantage. She broke again in the seventh game and held serve to close out a challenging test in two hours, six minutes.
In other matches, 12th seeded Spaniard Carla Suarez Navarro battled to a 7-6 (5) 3-6 6-1 win over Briton Heather Watson.
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