A heavy-footed and rusty Murray had to dig himself out of a number of holes before securing a 7-5 7-6(5) 6-2 win over the 95th-ranked Ukrainian, having spent far longer under a hot sun than he would have liked at Rod Laver Arena.
"I don't think it was the best match, to be honest," Murray told reporters after the two hours and 47 minute slog.
Murray has typically started the year's first grand slam like a well-oiled machine but for the first two sets the only free movement came from the Scot's vocal chords as he berated himself constantly for limp baseline play and wayward serving.
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"Shocking!" Murray howled at the terraces a number of times as he blew a 5-2 lead in the first set.
The 29-year-old was so agitated that he became confused by his drink bottles during a change of ends, unable to differentiate between a 600ml container and a much larger one.
"I know how much I have to drink when it's a certain temperature. I couldn't find how big it was, so I didn't know how much I was having to drink," he said with a sheepish smile as he studied his drink bottle in the post-match news conference.
"I still didn't see (the volume) on the court, but I can actually see it now. It's one litre."
Murray landed less than half his first serves in the match and was broken three times by Marchenko, who was buoyed by the Scot's troubles and swung hard for the lines.
But Murray yelled his way out of the rough patches and gradually shed his tentative ways to rally with aggression.
After edging the second set tiebreak, Murray roared to 5-1 in the third before progressing to a match against Russian qualifier Andrey Rublev who beat Taiwan's Lu Yen-Hsun.
He was not announced as "Sir Andy Murray" when he entered the court to a warm ovation but the Scot, bidding for his first Australian title after losing five finals, had no problem with that.
"Everyone around tennis, everyone that I know has been exactly the same," he said.
"I don't feel like it's been a distraction. It's something I've had to speak about, obviously quite a lot. But I've had enough time to get my head around it."
(Editing by Greg Stutchbury and Ed Osmond)
