The 24-year-old home player had not played a competitive match since February last year due to the corona pandemic.
She stood over the US Open and did not defend her title in the French Open, which was moved from early summer to autumn.
The top-seeded Barty, who had to give up the first round, decided on his fourth match ball against the 92nd-ranked Romanian with a serveess.
- I had so much fun out there and I have missed you so much, Barty said to a handful of fans at Melbourne Park where the Australian Open will also be played next week.
One of my favorite places in the whole world
- This is one of my favorite places in the whole world, Barty continued, who in the next round will meet the Czech Marie Bouzkova.
The reigning champion of the Australlian Open, the American Sofia Kenin, won in a snotty way.
She won the first set against the Italian Camila Giorgi with 7-5, when the Italian felt a thigh injury and broke the match.
"Obviously that was not the way I wanted to win the match and I hope she will be able to play the Australian Open," Kenin told Reuters.
If there were a handful of fans who showed up today, there will be thousands when the Grand Slam tournament begins next week.
The organizer will allow 30,000 spectators per day, which is half the capacity.