New cases dropped by 666 from Sunday and there were 14 fewer deaths.
There are 1288 patients in hospital, 74 of them in intensive care.
International travellers began arriving in Sydney early on Monday - for the first time without the need to quarantine - in more than two years.
However, they were confronted by the shutdown of all trains on the Sydney network, with industrial action benching intercity trains from Newcastle, Central Coast, the Blue Mountains and the Illawarra.
The NSW government and the union are blaming each other for the commuter chaos but Prime Minister Scott Morrison said the Rail Tram and Bus Union has marred an important milestone for Australia's tourism industry.
"The union movement has decided to really pull the rug our from under that on our first day back," he told Sydney radio 2GB.
"International travel is opening up from today and the unions welcome them with a train strike, I mean this is not how things should be done," he said.
The first of 56 international flights of vaccinated travellers touched down from the US just after 6am and were greeted by an elated Federal Tourism Minister Dan Tehan, holding a stuffed koala, Vegemite and Tim Tams.
"It's a great day, a great day to be out here," he told ABC TV.
"It is fantastic to be fully reopened to the rest of the world ... it is party time," he said.
Mr Tehan is confident the border reopening will prompt "a very strong rebound in the tourism market", and rejuvenate an industry that employs 660,000 people.
Meanwhile, testing of NSW schoolchildren will move to an on-demand basis from next week as the state further relaxes restrictions.
Students had been required to be tested twice a week, but will only need a test if they have symptoms or if necessary for other reasons.
Premier Dominic Perrottet on Sunday said parents would receive eight rapid antigen tests per student, to be distributed in two drops.
"The packs are there for families and staff to use at their discretion for their own peace of mind, for example, when a student is feeling unwell with a sore throat or cough, or if family members are sick," he said.
Teachers and early childhood staff will also receive the free tests.
NSW has recently scrapped QR code check-ins and the ban on singing and dancing in hospitality venues, as part of a broader push to relax restrictions after daily case numbers fell.
The requirement to wear face masks will mostly end on Friday, with them to remain mandatory on public transport, at airports and on planes, as well as in hospitals, aged and disability care centres.
