New York - Venus Williams moved into a potential US Open third round duel with sister Serena on Wednesday as a sexism row and extreme heat pushed the Grand Slam event to boiling point.
Williams, 38, notched up her 775th career win by seeing off Italy's Camila Giorgi 6-4, 7-5 as temperatures again climbed towards a sweltering 35 degrees.
The 2000 and 2001 champion in New York will face Serena for a place in the last 16 if the six-time winner gets past Germany's Carina Witthoeft under the Arthur Ashe Stadium lights later in the day.
"The last time we played in Australia it was two against one so this time it will be fair," joked Venus of her most recent meeting with her sister at the 2017 Australian Open, when Serena won the title despite being in the early stages of pregnancy.
With her win on Wednesday, Venus is through to the third round in New York for the 17th time.
"I was happy to complete the match in the shade. I'm pretty pumped to get through," added Venus, playing in her 80th Grand Slam event.
Defending champion and third seed Sloane Stephens also made the third round with a marathon 4-6, 7-5, 6-2 win over Ukraine qualifier Anhelina Kalinina.
Stephens triumphed after 2 hours and 46 minutes on Arthur Ashe Stadium and will next face two-time Australian Open champion and former world number one Victoria Azarenka.
The American needed treatment on a blistered right hand in the second set as the crushing effect of the heat and humidity took its toll.
However, the 10-minute heat-break between the second and third sets proved a timely boost.
"I just sat on the floor, changed my outfit, had two bites of Sushi and a slushie," said the 25-year-old Stephens after seeing off world number 134 Kalinina.
"It was super-hot so I'm just happy to be through."
Azarenka, the 2012 and 2013 runner-up, made the third round for the first time in three years with a 6-1, 6-2 win against Australian 25th seed Daria Gavrilova.
Azarenka was amongst the first players to condemn the United States Tennis Association (USTA) for handing French player Alize Cornet a code violation for changing her shirt on court on Tuesday.
The incident sparked an immediate storm over sexism.
The Belarusian said the USTA displayed double standards for sanctioning Cornet while male players routinely remove their shirts courtside as the heat and humidity bite.
"If I would say my true feelings, it would be bleeped out, because it was ridiculous. It wasn't anything disrespectful," said Azarenka.
The USTA admitted they were wrong to hand Cornet a warning for slipping off her shirt on court after realising she had put the garment on back-to-front during a heat break.
The WTA said Cornet "did nothing wrong" as the USTA went into damage limitation.
"We regret that a code violation was assessed to Ms. Cornet yesterday," said the USTA in a statement.
"We have clarified the policy to ensure this will not happen moving forward. Fortunately, she was only assessed a warning with no further penalty or fine."
Ukraine seventh seed Elina Svitolina was also an early winner on Wednesday, cruising past Tatjana Maria 6-2, 6-3 to avenge a first round defeat at the hands of the German player at Wimbledon last month.
US Open results on Wednesday, the third day of the 2018 tournament at Flushing Meadows (x denotes seeded player):
Borna Coric (CRO x20) bt Roberto Carballs Baena (ESP) 7-6 (7/4), 6-2, 6-3
Daniil Medvedev (RUS) bt Stefanos Tsitsipas (GRE x15) 6-4, 6-3, 4-6, 6-3
Milos Raonic (CAN x25) bt Gilles Simon (FRA) 6-3, 6-4, 6-4
Stan Wawrinka (SUI) bt Ugo Humbert (FRA) 7-6 (7/5), 4-6, 6-3, 7-5
Venus Williams (USA x16) bt Camila Giorgi (ITA) 6-4, 7-5
Sloane Stephens (USA x3) bt Anhelina Kalinina (UKR) 4-6, 7-5, 6-2
Victoria Azarenka (BLR) bt Daria Gavrilova (AUS x25) 6-1, 6-2
Barbora Strycova (CZE x23) bt Lara Arruabarrena (ESP) 6-0, 6-1
Elise Mertens (BEL x15) bt Vera Lapko (BLR) 6-2, 6-0
Anastasija Sevastova (LAT x19) bt Claire Liu (USA) 6-3, 6-1
Wang Qiang (CHN) bt Irina-Camelia Begu (ROM) 6-3, 6-1
Elina Svitolina (UKR x7) bt Tatjana Maria (GER) 6-2, 6-3