Suncream, hats and icepacks were the order of the day at Melbourne Park as temperatures crept steadily towards the 40 degrees Celsius mark on the fourth day of play at the year's first grand slam.
Third seed Williams did her best to keep her time on court to a minimum as she swept aside Garbine Muguruza 6-2 6-0 before Murray, her counterpart in the men's draw, kept his cool to despatch Joao Sousa 6-2 6-2 6-4 on Hisense Arena.
Of the 17 matches played on the main showcourt Rod Laver Arena in the tournament so far, only one has not been won in straight sets and even a split lip from her own racket was not going to stop Williams continuing that trend.
Victoria Azarenka may be defending champion and world number one but Williams is odds-on favourite to capture a 16th grand slam title and a sixth in Australia next week.
The Belarussian proceeded easily enough with a 6-1 6-0 thrashing of Eleni Daniilidou but any hopes she had that Williams, against whom she has a 1-11 record, might be hampered by the ankle she injured on Tuesday were quickly dashed.
The American dabbed her lip in pain after a forehand follow-through hit her in the mouth during the first set against the lowly-ranked Spaniard, but was barely troubled thereafter and set up a meeting with Japan's Ayumi Morita with her 10th ace.
"I didn't feel anything today," the 31-year-old said of the ankle injury. "Obviously when you go out to play you're heavy on adrenaline and you're really pumped up.
"Usually I feel injuries after the match, but so far, so good. I felt much better than I ever dreamed of expecting to feel.
"I'm on the up and up. It can only get better from here."
The outer courts were again the place to go to see upsets with Lithuanian Ricardas Berankis hammering 25th seed Florian Mayer 6-2 6-3 6-1 on court six, while women's 21st seed Varvara Lepchenko was a 6-4 6-2 victim of Elena Vesnina on court two.
Jo-Wilfried Tsonga looked to be wilting in the sweltering heat of Margaret Court Arena when Go Soeda was 5-3 up and serving for the second set but the French seventh seed recovered to slap down the Japanese 6-3 7-6 6-3.
Tsonga, losing finalist here five years ago, was not happy with his performance but was not about to blame the heat.
"You have to deal with it. That's it," he said.
Berankis's win means he will be Murray's next opponent and the convincing nature of his win over Mayer indicated that he might prove trickier for the Scot than the game but limited Sousa.
Murray unveiled his full repertoire of shots in the 101-minute contest and every one was superior to that possessed by his Portuguese opponent.
The 25-year-old stuttered a little as he looked to close out the match in the third set but fired down his 14th ace to bring up match point before clinching the victory when a Sousa return went long.
"It doesn't matter how much training you do, it always difficult when the sun comes out here," Murray said.
"You need to get in control of the points and dictate them because otherwise you will get very tired very quickly in these conditions."
The victories for Williams and Azarenka continued the trend for lop-sided scores in matches involving the top four women, none of whom has dropped a set yet.
"I think I honestly can only speak for myself, but it seems like everybody is in great form, and it's going to be very interesting," said Azarenka.
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