Naomi Osaka held her nerve, despite squandering two match points late in the deciding set, to secure a clash against Katerina Siniakova of the Czech Republic.
Ashleigh Barty leads Australia's hopes of reaching a first Fed Cup final since 1993 when they face 2017 runners up Belarus in Brisbane.
Serena Williams beat Victoria Azarenka 7-5, 6-3 in an electrifying Indian Wells clash of former world number ones.
The former world number one was dumped from the season-opening Grand Slam in a gut-wrenching loss to little-known German Laura Siegemund late Tuesday.
Victoria Azarenka suffered a 6-7 (5/7), 6-4, 6-2 defeat against Germany's Laura Siegemund in the first round.
Roland Garros organisers have come under fire for not seeding 23-time major champion Williams for the French Open.
Petra Kvitova is one of the favourites to win a maiden French Open title after winning four titles this season, including on clay in Prague and Madrid.
Sloane Stephens will enter the top 10 for the first time next week when the WTA rankings are announced.
Victoria Azarenka reached the US Open final in 2012 and 2013 where she was beaten by Serena Williams on both occasions.
Rafael Nadal dismissed Karen Khachanov in straight sets, Victoria Azarenka got the better of British hope Heather Watson in three sets.
With the 23-time Major winner preparing for the birth of her first child and the Russian out with an injury, the race to the Venus Rosewater Dish is wide open.
Former world No 1 will return to competition seven months after giving birth to son Leo.
Serena Williams will again be the cynosure of the women's singles competition in the Australian Open. She will face Switzerland's Belinda Bencic in a difficult first-round clash on Monday.
Victoria Azarenka had to retire from her opening round tie against Karin Knapp at Roland Garros with the knee problem
Nick Kyrgios defeated 2014 Madrid Open finalist Stan Wawrinka while Victoria Azarenka withdrew from the tournament due to a back injury.
Victoria Azarenka and Petra Kvitova won in straight sets to enter the Madrid Open third round
With the world's dominant player Serena Williams missing for so much of the season, 16 different women have already lifted WTA titles this year with Sloane Stephens, Victoria Azarenka and Angelique Kerber the only multiple winners.
Victoria Azarenka beat two-time Grand Slam champion Svetlana Kuznetsova of Russia 6-3, 6-2 for her third Miami Open title.