The 31-year-old Murray ended his season early last year after suffering pain in his hip following surgery earlier in 2018 that ruled him out of three of the four Grand Slam events.
Murray, whose ranking has dropped to 240 and was unseeded in Brisbane, had earlier said he was still feeling pain in his hip but was in a "better place" than he was 12 months ago.
'I don't enjoy tennis as much' - Murray admits comeback is proving tough
"I was a bit nervous. But as the match went on I thought I moved well," Murray said on Eurosport after his 10th successive win in Brisbane, having won the tournament at both his previous appearances in 2012 and 2013.
"It's my first match after a big break. It's not easy to sum up (but) it's been really hard the last 18 months, been a lot of ups and downs trying to get back on court.
Emotional Murray: I don't know how much longer it's going to last
"Being back now I am trying to enjoy it as much as I can, for as long as I can because I am not sure how much longer I have got."
Murray returned to the court last June and played just 12 complete matches last year.
'Up and running' - Murray wins comeback match in Brisbane
As an unseeded player in Brisbane he has a tough draw, with a second round clash with Russian fourth seed Daniil Medvedev.
'It's a no-brainer' - Murray urges players to support vaccine
Novak, put your money where your mouth is: Appearance fees have to end