Murray cut a frustrated figure as he battled his way past Illya Marchenko in straight sets, shouting up to his box on numerous occasions, but he never looked like missing the opportunity to progress.
The world number one had to contend with very troublesome conditions as the sun blazed down on Rod Laver Arena, but he found just enough class to come through the tricky opening encounter - all while his wife Kim Sears battled away with the 'player box' cam.
Venus, meanwhile, was on very fine form as she overcame Kateryna Kozlova, playing some superb tennis before producing one of the most memorable post-match interviews at Melbourne Park.
Venus was in no mood to let interviewer Sam Smith get away with joking about her age, firing back in humorous and pretty cutting fashion.
Sadly for Simona Halep, she was not in as high spirits as Venus as she trudged away in heartbreaking fashion after suffering a first-round exit to world number 52 Shelby Rogers.
It was hard to watch Halep walk off court with a hood over her head, and then to have to walk down a tunnel with the faces of past winners plastered all over the walls.
With Roger Federer, Stan Wawrinka, controversy's Nick Kyrgios and defending champion Angelique Kerber still to come, the opening day in Melbourne is just getting started.
Monday's highlights
Andy Murray secures his place in the second round after a straight sets victory over Illya Marcheko in searing Melbourne heat.
Venus Williams survives a rocky start to reach the second round of her 17th Australian Open, beating Kateryna Kozlova 7-6 7-5
Seventh seed Garbine Muguruza battles through an injury to overcome Marina Erakovic 7-5 6-4.
Fourth seed Simona Halep suffers a shock defeat to world number 52 Shelby Rogers 6-3 6-1.
Olympic champion Monica Puig hammers Patricia Tig 6-0 6-1 for the first completed match of this year's tournament.
American Varvara Lepchenko produces an upset over last year's French Open semi-finalist Kiki Bertens, beating the Belgian 19th seed 7-5 7-6(5).
Britain's Aljaz Bedene loses 7-6 7-5 0-6 6-3 to world number 103 Victor Estrella Burgos to exit in the first round.
Kei Nishikori is forced to dig deep with the world number five taken the distance by Russia's Andrey Kuznetsov before eking out a 5-7 6-1 6-4 6-7(6) 6-2 win.
Coco Vandeweghe collapses to the ground after sealing her place in the second round of the Australian Open having battled an illness, 6-1 7-6 over Roberta Vinci.
Britwatch
Aljaz Bedene suffered a very disappointing four-set defeat to world number 103 Victor Estrella Burgos of the Dominican Republic.
Bedene had been tipped to make a surprise run in Melbourne but, as Eurosport commentator Simon Reed reflected, he "made way too many mistakes" when it really mattered.
It is the fifth time in a row Bedene has lost in Melbourne in the opening round while world number 103 Estrella Burgos goes through to face Australian Bernard Tomic.
Meanwhile, as mentioned above, Andy Murray made it through in straight sets with victory over Illya Marchenko in very tough conditions.
The heat proved a real issue throughout the match, but Murray battled his way through to a second-round clash with qualifier, Russia's Andrey Rublev.
Daniel Evans is also in action against Facundo Bagnis, seeking to secure his place in the second round.
Stat of the day
Poor Simona Halep - this stat really puts the enormity of her shock first-round defeat in context:
Respect
Coco Vandeweghe collapsed to the ground after sealing her place in the second round of the Australian Open having battled an illness.
It was a highly emotional moment as Vandeweghe was helped at her chair by medical staff and the crowd gave her their full support.
The image of the player shaking on the ground having secured victory over Roberta Vinci of Italy was a very powerful one.
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