The Hong Kong Observatory raised the second highest storm warning -- a number nine signal -- at 8:10 pm (1210 GMT), after the number eight signal forced the closure of schools, shops, businesses and financial markets in the early afternoon.
Strong winds that preceded the typhoon -- which was expected to be closest to the territory around midnight (1600 GMT) -- knocked down at least eight trees, officials said, as large waves crashed into the coastline.
There had also been some minor flooding and two minor landslides, but there were no reports of injuries, they said.
Authorities urged people to go home once signal eight was raised, sending thousands of people streaming out of their offices to catch last-minute ferries or buses before public transport was suspended.
Throngs of schoolchildren packed fast food restaurants and huddled under umbrellas at bus stops as they waited to get home while workers hastily took down advertising signs and lashed down bamboo scaffolding.
But by nightfall the city was all but deserted, with shops fastened shut, ferries suspended and only limited bus and rail services in operation in lashing rain.
At the Hong Kong International Airport, the typhoon caused the cancellation of 134 flights while 94 had been delayed by 5:30 pm, authorities said.
The government said it had opened 27 temporary shelters, to which more than 120 people had been admitted by early evening.
At 8:00 pm (1200 GMT) Dujuan was was about 70 kilometers (43 miles) east-northeast of Hong Kong and forecast to move west at about 30 kilometers per hour towards the Pearl River Estuary of southern China.
Weather authorities said it was the strongest storm so far this year and was packing winds of 80 knots (140 kilometres) per hour, with gusts of up to 120 knots (180 kilometres) per hour.
A Hong Kong Observatory spokesman said the typhoon was unusual in that it appeared to have two eyes, one about 20 kilometres in diameter and the other 210 kilometres.
The typhoon brushed southern Taiwan overnight leaving more than 500,000 homes without electricity at one point and severely interrupting road, rail and air links.
One man drowned off the island of Penghu, while another person was missing after being washed away by flood waters in mountainous Taitung county.
Hong Kong regularly suffers torrential rain and flooding from typhoons that pass by the territory each year, although direct hits are rare.
The most devastating in Hong Kong's recorded history was the "Great Typhoon" of September 1937, which sank thousands of junks and cargo boats and killed more than 10,000 people.
One of the worst in recent history was Typhoon Wanda in 1962, which claimed more than 130 lives, left dozens more missing and wrecked around 1,000 boats and ships.
Typhoon Dujuan wreaked havoc after roaring past southern Taiwan overnight Monday.
The storm left 549,349 households in darkness, with power supply to 157,000 homes still interrupted as of Tuesday morning, according to the National Fire Agency's disaster command center.
Torrential rains continued to batter southeastern and southern Taiwan as well as the mountainous areas in northern, central and northeastern parts of the island, the Central Weather Bureau said.
The one fatality was identified as 54 year-old Lin Tze-rong, while the missing person was named as 23 year-old student Yen Min-ju, who was swept away by flood water while conducting research in a mountainous area of eastern Taitung County.
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