"Ever since then, I've been trying to have a very positive outlook on everything. I think that's really been helping me, even in tough situations."
Williams, a 23-time Grand Slam champion, slid from No 8 to No 9 after losing her second consecutive US Open final — and finishing as the runner-up for the fourth time in the past six majors.
Osaka, last year's champion, and Barty both lost in the fourth round. That allowed Barty to move up from No 2 and Osaka dropped to No 4. Barty already briefly was No 1 after winning the French Open in June for her first major championship.
Karolina Pliskova is No 2, and Elina Svitolina is No 3.
US Open men's champion Rafael Nadal stayed at No 2 in the ATP rankings and closed the gap between him and No 1 Novak Djokovic.
Runner-up Daniil Medvedev is up to a personal-best No 4 from No 5 after reaching his first Grand Slam final, where he lost to Nadal 7-5, 6-3, 5-7, 4-6, 6-4 over nearly five hours.
Nadal collected his fourth trophy in New York and his 19th Grand Slam title in all, moving within one of Roger Federer's record for men.
Federer remained at No 3 after losing in the quarter-finals while bothered by a bad back.
- AP