Having slept for fewer than six hours the night before, he steered the Megisti under power across the harbour, planning to arrive at the Seaview Marina next to Point Howard at about 8am.
But shortly after changing course at the southern end of Matiu/Somes Island, he fell asleep.
Megisti continued under autopilot until colliding with the wharf, which woke Newman.
The collision caused significant damage to Megisti but only minor damage to the wharf.
The wharf carries a fuel line used to offload oil from tankers berthed in Wellington Harbour. There was no damage to the fuel line, nor any oil spill or fire.
Maritime NZ said Newman was asleep for about 20 minutes as Megisti motored with no one in control through one of the busiest parts of the harbour used by kayakers, boaties, cross-harbour ferries and oil tankers.
"It was just pure good luck that no one was hurt or killed," central compliance manager Michael-Paul Abbott said.
"Fatigue is a major problem on ships. Tired crew put themselves and others in serious danger.
"We are working with the maritime industry to help crews find better ways to manage fatigue but where reasonable steps are not taken and people or property are put at risk, then Maritime NZ will take action."
Newman pleaded guilty to one charge under the Maritime Transport Act of operating a ship in a way that caused unnecessary danger or risk to people and property.
He was sentenced in the Wellington District Court on Friday afternoon.