Williams, who lost nine sets, including seven first-set losses, in her charge to the Australian, French and Wimbledon titles, was tested at Flushing Meadows by her fellow American, but roared back to victory to reach the fourth round.
"I'm not trying to live on the edge," the 33-year-old Williams said in an on-court interview. "I'm playing players that come out really strong. I just think Bethanie played really well."
The world number one looked out of sorts at the start, broken twice in dropping the first set to the aggressive Mattek-Sands, who at age 30 still looks like a punk rocker with a splash of orange topping her pinned up blond hair.
Williams at times appeared to be trying too hard, putting extra effort into opportunities to produce a service break and often overhitting and sending shots wide or long.
She won only one of seven break points in the first set, and two of nine in the second.
A service break by Williams in the last game of the second set, on her second set point, forced the decider and by then Williams seemed to have relaxed and produced the prodigious power that has carried her to a 51-2 record this year.
"She's a great player. She's fought so many difficult injuries," Williams said of Mattek-Sands. "I respect her a lot and know to expect a great game."
Mattek-Sands tumbled down the singles rankings after a string of serious injuries, including two hip surgeries, a foot fracture and a partial tear of the patella.
But she has come back to thrive at doubles. This year winning women's doubles titles at the Australian and French Opens and the mixed doubles crown at Roland Garros.
Williams was proud of her own fighting spirit, while acknowledging she had struggled to convert break points.
The 21-times grand slam singles winner, who is aiming to join Maureen Connolly (1953), Margaret Court (1970) and Steffi Graf (1988) as the only women to sweep the four grand slams in a single season, next faces fellow American Madison Keys.
Keys advanced 6-3 6-2 over 15th seed Agnieszka Radwanska of Poland.
(Reporting by Larry Fine; Editing by Mark Lamport-Stokes)
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