"For me, I stay positive because I know I can play great tennis," Williams said. "Sometimes you just have to go through more than what you want to go through. Sometimes you have to have losses. When I had losses, it always motivates me a lot to do better and to work harder."
The 33-year-old looked strong Monday, purple braids poking out of her visor that matched her floral dress. Williams fought off three break points at 2-2 in the second set in a game that went to six deuces.
Bothered by a lower back injury, Williams was playing just her third event since a first-round loss at the French Open. She hadn't defeated a top-20 opponent since last October.
Flipkens, meanwhile, had been enjoying a career year. The Belgian had never reached the round of 16 at a major tournament before the Australian Open, then made her run at Wimbledon.
Rafael Nadal's stay at Wimbledon ended in his opener. In his first Grand Slam match since and first U.S. Open since 2011 the second-seeded Spaniard rolled past American Ryan Harrison 6-4, 6-2, 6-2.
American Sloane Stephens, seeded 15th, rallied from a set down to beat Mandy Minella of Luxembourg 4-6, 6-3, 7-6 (5).
In the day's first big upset, a British man not named Andy Murray 179th-ranked qualifier Daniel Evans stunned 11th-seeded Kei Nishikori in straight sets. Evans won 6-4, 6-4, 6-2 in his U.S. Open debut.
Later Monday, rain postponed 17-time major champion Roger Federer's match against 62nd-ranked Grega Zemlja until Tuesday.
P Tuesday, 11 a.m. and 5 p.m.
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