Residents of Darwin and surrounding regions have been urged not to panic but to stay in their homes or emergency shelters until given the all-clear.
The strengthened category-three system brought destructive wind gusts to remote Tiwi Islands communities after passing over the Cobourg Peninsula overnight into the Van Diemen Gulf.
Forecasters expected Fina to track just north of Darwin, which would cop destructive winds and heavy rain, with the risk of flooding.
NT Police incident controller Kirsten Engels said the situation was serious, but people should not panic.
Everyone should stay in their homes or public shelters until emergency services declared it safe to leave, she said.
"Don't panic, enact your plans, we've got this," Superintendent Engels said.
"We're prepared and we're ready and we're in this together."
Emergency shelters were open in Darwin, nearby Palmerston and adjacent rural areas, with people urged to bring their own bedding and food.
Bureau of Meteorology NT manager Shenagh Gamble said Fina was a "small and intense" system that would bring wild weather to Darwin and surrounds.
"We will see conditions worsen further and it will be worsening quickly," she said on Saturday afternoon.
"So as we approach this evening and the sun goes down, conditions are going to deteriorate significantly."
Ms Gamble said conditions would ease considerably from Sunday morning.
As the wind and rain ramped up in Darwin, trees were being stripped of their leaves and some areas experienced power cuts, with crews working to restore services.
Heavy rainfall could lead to flash flooding in coastal areas between the Tiwi Islands and Warruwi, extending across the western Top End including Darwin on Saturday and Sunday.
Senior meteorologist Dean Narramore said 150 to 180km/h category three winds would be near the centre of the cyclone and hopefully stay over the water.
But Darwin could still experience winds of up to 120km/h.
Those wind strengths were "easily enough to cause property damage and bring down trees and powerlines", Mr Narramore told ABC News.
Some island locations have copped 200mm of rain in 24 hours and similar falls were expected in the Darwin area.
Mr Narramore said the impacts were highly dependent on the exact track and intensity of Fina.
"If it moves a bit further north, less impacts for Darwin, more impacts for the Tiwi," he said.
"But if it wobbles a little bit further south ... we could see more impacts in Darwin."
Alice Williams, the office co-ordinator for the Tiwi Islands Regional Council at Milikapiti, near the most northerly reach of the territory, told AAP the winds were picking up and some people were a "little bit anxious".
Sirens were ready to activate, so the community knew the weather was worsening and it was time to shelter, she said.
The community of about 500 had plenty of food, water and fuel and two extra police officers were on hand to assist.
People had moved to shelters in the council office and primary school on Friday evening, while others chose to stay at homes deemed safe, Ms Williams said.
Conditions are set to ease in the Top End by late Sunday as the system moves to Western Australia.
Cyclone Tracy was the most devastating system to hit Darwin, killing 66 people on Christmas Day, 1974.
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