Serena holds off young rival to make last eight NEW YORK (Reuters) - Defending champion Serena Williams overpowered Sloane Stephens 6-4 6-1 on Sunday to reach the U.S. Open quarter-finals and exact revenge for her shock Australian Open loss to the young American. Williams, who was upset by Stephens in the last eight at Melbourne Park, swatted the 20-year-old aside on Arthur Ashe Stadium's center court with a brilliant display of power tennis. While Stephens has been touted as the next queen of U.S. women's tennis, 31-year-old Williams showed no signs of giving up her throne in a fourth-round encounter with the atmosphere of a championship decider. "It definitely feels like a real big match," Williams said on-court to a crowd divided in its loyalties. "How excited are we about the future of American tennis?" the world number one asked, drawing roars from the stands. It definitely felt like something bigger. Williams, bidding to become the oldest U.S. Open women's champion since tennis turned professional in 1968, broke Stephens in the 10th game to end a riveting first set when a big forehand from the 15th seed sailed just wide. The 16-times grand slam winner then raced through the second to set up a clash with 18th-seeded Spaniard Carla Suarez Navarro who took down eighth seed Angelique Kerber of Germany. The quality and tension of the showdown between Williams and Stephens, one of the few in women's tennis capable of trading blows with equal ferocity, thrilled the stadium crowd and left both players impressed. "I thought I played good," Stephens said. There were times I played some really good tennis. Second set got away from me a little bit, but overall I thought I played great. Williams drew first blood by breaking serve to lead 4-2 before the heavy-hitting Stephens broke back with the help of two double faults. Serving at 4-5 to stay in the set, Stephens fought off two set points before caving in. Williams fended off a break point in the first game of the second set and it was smooth sailing from there, as she kept up the pressure to deny Stephens any hope of a comeback. Williams, whose relationship with Stephens grew icy after their Australian Open encounter, kept herself charged up with fist pumps and shouts of "Yes!" and "C'mon!" When she broke serve in the fourth game of the second set with an overhead at Stephen's feet that bounced up to hit her, Williams did not bother with a wave of apology and simply turned to walk away. "At the end of the day it was a fourth round match (even though) it definitely had feelings more of a quarter-final or a semi-final match," Williams said. Stephens, who reached the Australian Open semi-finals and quarter-finals at Wimbledon this year, said she was not bothered about being proclaimed heir apparent to fellow African American Williams. "I embrace it," she said. Right now I'm carrying the little torch. But I'm OK with it. I embrace it for now. Reporting by Larry Fine; editing by Gene Cherry and Ian Ransom