The 28-year-old Muguruza was previously ranked third back in July 2018, while her compatriot Paula Badosa, whom she beat in the semi-finals, also leapt two spots to go eighth
The 28-year-old Spaniard beat Anett Kontaveit 6-3, 7-5 to improve her record playing in Mexico at 14 wins and two losses
Anett Kontaveit will face Garbine Muguruza in the final of the season-ending WTA Finals in Guadalajara after both women battled through the semi-finals in contrasting fashion
Muguruza's victory in her final round-robin contest in the eight-woman season finale in Guadalajara denied Karolina Pliskova a place in the knockout phase
To qualify for the semi-finals for the second time in her career, Garbine Muguruza (1-1) needs a win on Sunday against Kontaveit (2-0) and a Krejcikova victory over Pliskova (1—1).
Anett Kontaveit continued her late-season surge, notching her 12th straight WTA match win as she assured herself of finishing in the top two of her group
Pliskova is playing the WTA Finals for the fifth time, having reached the semifinals in 2018 and '19. The 2020 tournament was cancelled.
Kremlin Cup 2021: Aryna Sabalenka knocked out by Ekaterina Alexandrova, Maria Sakkari beats Simona Halep
Sabalenka was playing in her first tournament since reaching the semi-finals of the US Open last month. She then missed the tournament in Indian Wells, California, after a positive test for the coronavirus.
Medvedev didn't face a break point, and converted three of his seven break chances against the American to wrap things up in 72 minutes.
The rebranded Fed Cup tournament will be held on indoor hard courts at Prague's O2 Arena on 1-6 November after the Czech capital replaced Budapest as the host city earlier this year.
Spanish second seed Muguruza, who turns 28 on Friday, took her ninth career WTA title and second tour crown of the year after Dubai in March.
The Tunisian won her 43rd match of the year, tying her with second-ranked Aryna Sabalenka for the most on the WTA Tour.
The 18-year-old became the first player to emerge from qualifying to win a Grand Slam tournament when she beat another teenager, 19-year-old Canadian Leylah Fernandez, 6-4, 6-3 on Saturday.
Garbine Muguruza did not like how her topsy-turvy fourth-round match at the US Open against Barbora Krejcikova ended. And that was not just because Muguruza lost.
Day 5 of US Open had its share of fantastic matches and upsets with Tsitsipas, defending champion Osaka and Rublev exiting the tournament.
Fernandez, who won her first WTA title in March at Monterrey, had never beaten so high-ranked a rival as third-rated Osaka and the same was true for Alcaraz when he sent home the men's world number three.
Tsitsipas registers another victory, Muguruza and Medvedev move further. Check out the key moments from US Open 2021
US Open 2021: Tsitsipas advances to third round after another long bathroom break; walkover for Osaka
The 23-year-old Greek third seed was booed after taking more than eight minutes between the third and fourth sets but dominated after his extended toilet trip to flush Frenchman Adrian Mannarino 6-3, 6-4, 6-7 (4/7), 6-0 at Arthur Ashe Stadium.
Osaka seeking her fifth career Grand Slam title and third US Open crown in four years, plays a second-round match against 145th-ranked Serbian qualifier Olga Danilovic.
Andreescu, the 2019 US Open champion, who missed the entire 2020 season with injury, has played little in 2021 and hadn't won a match since reaching the second round at Eastbourne in June.