The centre of the storm, with winds of up to 145 km/h (90 mph), moved more quickly than expected across the northern tip of the island.
Two people were reported missing, as 1,500 residents in villages vulnerable to flash floods were evacuated.
The typhoon is predicted to reached China's Fujian province on Sunday morning.
A woman was feared drowned, after she went to watch high seas near the eastern coastal city of Hualien.
And a man picking herbs in mountains near the capital Taipei had gone missing.
Domestic flights and many train services were cancelled, although most international flights were still operating.
Tape and sandbags
By 0800 (midnight GMT) on Saturday, Sinlaku had reached 240km (150 miles) north-east of Taipei.
Typhoon Sinlaku had already passed over Japan's Okinawa islands - causing a number of injuries and damage to homes.
Five Filipino sailors who were missing, feared drowned, were found safe on Friday by Japanese coastguards, according to AFP.
Residents in Taiwan sealed their windows with tape, and protected their doors with sandbags.
Last year Taiwan was hit by two severe typhoons.
Typhoon Toraji killed about 200 people in central and eastern Taiwan, when it struck in July.
And in September, Typhoon Nari killed almost 100 Taiwanese.