The Russian fifth seed started strongly by winning 10 of the first 11 games and after her Romanian opponent rallied in the second set to tie it up at 4-4, Kuznetsova broke again in the ninth game and served out the victory in 77 minutes.
"I started the year quite good with the feeling," the 31-year-old double grand slam winner told reporters.
Strycova wins thriller against Wozniacki in Sydney
"Sometimes the results don't go together with whatever you feel. But I feel very good for the start of the year, and for me it's a very nice feeling.
"I never thought of defending my title or something like that. It's just another tournament -- the title I have at home and no-one will take it away from me. This is another year and another opportunity to play."
Kuznetsova will next face the winner of the match between local favourite Sam Stosur and fellow Russian Anastasia Pavlyuchenkova.
Elsewhere, Canada's Eugenie Bouchard, a former Wimbledon finalist, also won her opening match with a 7-6(1) 6-2 first round win over China's Zhang Shuai.
However, fourth seed Karolina Pliskova, who will climb to world number five following her Brisbane title win on Saturday, will not be able to aim for back-to-back victories after she pulled out of the event with a left inner thigh injury.
The Czech was joined on the sidelines by Ukraine's world number 14 Elina Svitolina, who withdrew citing a viral illness.
"I've had constant headaches for the last two days and unfortunately in today's hot weather it got even worse when I was warming up and my body wasn't ready to compete," Svitolina, who was seeded seventh, said.
With the Australian Open tennis starting in a week's time in Melbourne, Frenchwoman Alize Cornet also decided against risking a sore back and pulled out of the Hobart International, which she won last year.
Cornet was the runner-up in Brisbane after going down 6-0 6-3 to Pliskova in the final.
"I am very sad I am not being able to play the tournament at Hobart this year," she said in a video message on Twitter. "It was meaning a lot to me to come back here and defend my title but I have to be reasonable.
"My back is not doing great and I have just one week to get ready for the Australian Open. I hope I can make it on time."
Konta through to last four in Sydney
Konta through to Sydney quarter-finals