Four months after having back surgery, the three-times Australian Open runner-up cruised to victory over his 112 ranked opponent in 85 dominant minutes on Hisense Arena.
Having played only two competitive matches in the build-up, Murray was worried that he might be under-cooked but in temperatures that hit 42.2 Celsius (108 Fahrenheit) at one stage he was rarely troubled.
"I played well today," fourth seed Murray told reporters, in typically understated manner.
"Maybe didn't expect to play as well as I did today, but the signs have been good in practice. I started the match off very well and did everything solid."
Murray decided to have surgery on his back after 18 months of playing through pain and said he felt much freer on court against Soeda.
"Not every shot hurt my back before but on certain shots I'm a lot freer in the movement just now," he said. "I hope that continues.
"That was the whole point of having the surgery. So if I was still in pain and stiff and sore then I'd be a bit worried about the next few years.
"But I'm hoping it was the right decision. I felt freer today than I did for the last 18 months.
Murray was relieved that his match - the second of the day on the show court at Melbourne Park - was played largely out of the sunlight.
"I was a bit nervous before the match but obviously when the shadow comes across the court it cooled down a little bit," he said.
"Still, the air is extremely warm. I was glad to get off quickly."
Murray now plays Frenchman Vincent Millot after the world number 267 beat American Wayne Odesnik in five sets.
Odesnik was banned for two years after pleading guilty to importing human growth hormone (HGH) into Australia in 2010.
The ban was halved to a year after Odesnik reportedly gave "substantial assistance" to anti-doping authorities, since which he has been largely shunned in the locker-room.
Murray refused to be drawn on whether Odesnik should be allowed to play on the Tour but made his feelings known.
"I haven't played or practised against him before and I haven't seen any of his matches. So I'll try and watch a bit of video of his match from today to see how he plays.
"But I'm glad he won."
(Editing by Patrick Johnston)
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