Engineers investigated and found there was no serious problem so power was restored and the ship docked at Adelaide later in the morning.
One passenger named Ian told 2GB radio the conditions while the ship was drifting were "absolutely horrific".
"We're drifting. We've got no power, no water, no toilets, no cooking, nothing," he said.
"They've got auxiliary power to light the corridors but that is it. It's like a ghost ship, mate."
He said he and his wife were supposed to be on the "cruise of a lifetime".
"The ship's just going around in circles, it's being blown around by light breezes," he said.
"We're just completely buggered."
The ship, run by Cruise and Maritime Voyages, set off from Tilbury, London in October and travelled across the Pacific to New Zealand and Australia.
The ship will travel back to London via the Suez Canal and the Mediterranean in March.
A spokesman for CMV said: "MV Vasco da Gama went into a controlled precautionary blackout early this morning at approx 0545hrs whilst sailing in the vicinity of the Port of Adelaide.
"Local authorities were notified of the incident as a precaution by the ship's Captain.
"An alarm light on the engine control room's panel led the vessel's officers to initiate a controlled blackout as a precaution against damage to systems onboard and in order to investigate the alarm.
"All precautionary post-incidents checks were completed with no causes for concern identified. Power was fully restored later in the morning and the vessel resumed sailing towards the port of Adelaide per its scheduled itinerary.
"The 55,877 GRT Vasco da Gama is currently on a East Coast Discovery cruise with 828 passengers on board.
"The ship has an excellent record of reliability and all passengers on board were kept informed of the technical problem experienced.
"For guests booked on the next cruise (V003), please check-in as normal, but please be advised there could be a small delay."
