Qantas Flight 144, a Boeing 737 aircraft en-route from Auckland, made the distress call over the Pacific Ocean on Wednesday afternoon.
"While a mayday was initially issued, this was downgraded to a PAN (Possible Assistance Needed)," a Qantas spokesperson told AAP on Wednesday evening.
"The aircraft landed safely at around 3.30pm (AEDT) and is now being inspected by our engineers."
While "inflight engine shutdowns" are rare and concerning for passengers, pilots are trained "to manage them safely and aircraft are designed to fly for an extended period on one engine," Qantas said.
It said all 145 passengers disembarked the aircraft normally.
Photographs taken at the airport show one of the engines appearss to have a large panel missing from the engine cover.
ABC television showed the plane land safely at Sydney airport and being escorted by yellow airport fire appliances to a parking bay.
Passengers told reporters an engine failed but no one onboard appeared panicked during the flight.
"I kind of heard the little bang and then a bit of turbulence, and we just thought okay, this is a bit weird," passenger Sandika McAuley said.
"But we didn't really know anything until we landed, then we got told that there was a mayday call and the engine failed."
James Mearon said he didn't realise how serious the situation was until he saw cameras waiting for passengers outside the terminal.
"Yeah it definitely was scary," he said.
The main issue impacting passengers was that the air conditioning had stopped working, according to passenger Fiona Dunne.
"The aircon was gone so everyone was just frustrated and sweaty, I don't think there was that much panic," she said.
Earlier, NSW Ambulance said in a statement that its paramedics responded to a mayday alert issued by the troubled flight.
FlightRadar, an internet flight tracker, indicated the 10-year-old, twin-jet Boeing plane issued the distress call over the Pacific Ocean.
Federal Transport Minister Catherine King said she was relieved the plane had landed safely.
"Well done to the highly experienced crew for getting the plane safely home," Ms King tweeted.
A mayday call is issued when a flight is in grave and imminent danger and needs immediate assistance, according to Airservices Australia, the federal agency responsible for ensuring safe air travel.
Once the call is made controllers alert aviation rescue, firefighting and emergency services with details on how to respond. They also provide assistance to pilots.
"As a precaution Sydney Airport had emergency crews on stand-by including firefighters, ambulance and police," an Airservices Australia spokesperson told AAP.
Aviation expert Neil Hansford said Boeing 737s could fly and land on only one engine, noting that "Qantas has never had a passenger lost on a jet aircraft in its history".
"What you may well find when the aircraft lands is that it may be prudence, rather than an uncontrollable situation," he told told Sky News.