The Boeing 787-9 with 49 people on board took 19 hours and 16 minutes to fly from New York to Sydney, a 16,200-km (10,066-mile) route.
Next month, the company plans to test a non-stop flight from London to Sydney.
Qantas expects to decide on whether to start the routes by the end of 2019.
If it goes ahead with them, the services would start operating in 2022 or 2023.
No commercial aircraft yet has the range to fly such an ultra-long haul route with a full passenger and cargo load, Reuters news agency reports.
To give the plane sufficient fuel range to avoid re-fuelling, the Qantas flight took off with maximum fuel, restricted baggage load and no cargo
Passengers set their watches to Sydney time after boarding and were kept awake until night fell in eastern Australia to reduce their jetlag.
Six hours later, they were served a high-carbohydrate meal and the lights were dimmed to encourage them to sleep.
On-board tests included monitoring pilot brain waves, melatonin levels and alertness as well as exercise classes for passengers and analysis of the impact of crossing so many time zones on people's bodies.
"This is a really significant first for aviation. Hopefully, it's a preview of a regular service that will speed up how people travel from one side of the globe to the other," said Qantas Group CEO Alan Joyce.