As temperatures topped 32 Celsius (90 Fahrenheit), Murray came through a two hours, 47 minutes test against Ukraine's Illya Marchenko 7-5, 7-6 (7/5), 6-2.
He fared better than women's fourth seed Simona Halep, who was an early casualty, and Kei Nishikori and Marin Cilic, who were both taken to five sets.
Players draped themselves with towels packed with ice on a sweltering afternoon. Temperatures are set to rise further on Tuesday to a sizzling 38 Celsius.
Halep is rated as the fastest player, male or female, over three metres but her usual zip was glaringly absent as she went down 6-3, 6-1 to American rising star Shelby Rogers.
Afterwards she said a knee injury had slowed her down as she succumbed in the Australian Open's first round for the second consecutive year.
For 24-year-old Rogers, it was further proof of her potential after she reached last year's French Open quarter-finals and rose nearly 100 places in the rankings last year.
- 'I'm dying, I guess' -
========================
Venus Williams, the oldest player in the women's draw at 36, also found herself with a fight on her hands but she came through 7-6 (7/5), 7-5 against 22-year-old Kateryna Kozlova.
"Girl, I don't know," she told on-court interviewer Samantha Smith, who pointed out that Williams turned professional in 1994, the year that Kozlova was born.
"I know how to play tennis. I like to think I'm good at this. She hasn't had the years that I've had yet, the grey hairs and I'm dying, I guess. The wrinkles that I'm hiding... you're trying to make me feel old!"
Marin Cilic, the 2014 US Open winner, also needed five as he came from two sets down to dispatch Jerzy Janowicz 4-6, 4-6, 6-2, 6-2, 6-3.
China's Zhang Shuai, who made a surprise run to last year's quarter-finals, had an easier time with a 6-0, 6-3 win over Aliaksandra Sasnovich of Belarus.
Olympic champion Monica Puig stormed through 6-0, 6-1 against Patricia Tig and Jelena Jankovic, playing her 53rd consecutive Grand Slam, beat Laura Siegemund 6-1, 1-6, 6-4.
Federer, now 35, has a difficult draw and his first-round opponent on Monday is Austria's Jurgen Melzer, who won their last meeting -- albeit in 2011, in Monaco.
Angelique Kerber will launch her first Grand Slam title defence against Ukraine's Lesia Tsurenko as she attempts to cement her position on top of the world rankings.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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