Murray sped to a 6-3 6-1 victory over Norwegian Viktor Durasovic, a player ranked a lowly No.345 by the ATP, who won through two qualifying rounds to reach the main draw.
The Scot broke four times across the contest and won 25 of 26 points when landing a first serve, an encouraging rate. Realistically, anything other than a comfortable win for the former world No.1 would have been concerning ahead of the Australian Open.
Murray at least put last week's disappointing first-round loss to Facundo Bagnis at the Melbourne Summer Set tournament behind him, and now a stiff tests await him in the last 16 stage.
Georgian Nikoloz Basilashvili, the No.2 seed, is next for Murray on Wednesday, with the world No.23 a familiar foe after these two met in the first round at Wimbledon last July.
On that occasion, Murray won in four sets after a desperate wobble in the third, which he lost from 5-0 ahead.
Five times an Australian Open finalist, Murray believes limbering up this week in Sydney can set him up well for the season's first grand slam.
"It is perfect conditions here," Murray said. "It feels like you are playing indoors. It is really nice to get your range here, and hopefully I can carry that through to Melbourne.
"I was hoping to get matches in Melbourne last week, but that didn't happen. Thankfully the tournament organisers and Tennis Australia agreed to give me the wildcard and the opportunity to play here, and I am very grateful for that."
Tuesday also saw a win for Maxime Cressy, the American serve-volleyer who caused a stir with his run to last week's final in Melbourne before pushing eventual champion Rafael Nadal in the title match.
Cressy, who was born in Paris, is a throwback in an era dominated by baseliners, and his game again came good as he saw off Adrian Mannarino 6-3 7-5. Dusan Lajovic awaits him in round two after the Serbian beat Spain's Alejandro Davidovich Fokina 7-6 (7-5) 6-4.
At the Adelaide International 2 tournament, South Africa's Lloyd Harris, the No.5 seed, made a first-round exit, losing 5-7 7-5 6-4 to Soonwoo Kwon.
There was another positive performance from Adelaide's own Thanasi Kokkinakis, who swatted away Frenchman Benoit Paire 6-4 6-0 to tee up a second-round shot at American No.2 seed John Isner.
Kokkinakis, a once-bright young prospect who is finding his way again on tour after injury trouble, reached the semi-finals of last week's Adelaide tournament and is eyeing another run in South Australia before heading to Melbourne.
"After a good run last week, I was pretty knackered – I'm not going to lie," Kokkinakis said. "But I thought another one in my hometown was a perfect situation.
"It was kind of a win-win for me almost. If I won, perfect, I get more matches. If not, I get to Melbourne and get to prepare for Aussie Open, but I'm stoked with the win."