Australia’s Bureau of Meteorology said Dampier, with population of 1,000, was in the path of the cyclone's eye wall, packing destructive winds of up to 195 kilometres an hour.
A local State Emergency Services (SES) spokesman said power was out in most homes in Dampier and Karratha, the area's main population centre with 11,000 residents, but there had been no reports of injuries or structural damage.
The category three storm had originally been expected to cross the Pilbara coast between Dampier and Mardie, a cattle station south of the town, about 9pm WST, but it had slowed from 180 to 120 kilometres an hour and was expected three hours later.
Clare was now moving erratically as it interacted with the land, but was expected to resume a south-southwesterly track over the next few hours.
He said a destructive storm surge earlier expected to accompany the cyclone would not eventuate.
More than 1,500 people were evacuated from low-lying areas along the north-west coast when the surge had been expected to reach seven metres.
But the current forecast was for only a two to three metre tidal surge, the SES spokesman said.
A number of people in the low-lying areas refused to evacuate.
Residents in or near the communities of Karratha, Dampier, Roebourne, Wickham, Point Samson, Whim Creek, Nanutarra and Pannawonica remain on Red Alert and advised stay sheltered until further notice.
Widespread heavy rain and flooding are expected in the Pilbara and Gascoyne over the next few days.
Clare has forced the closure of shipping ports, Karratha airport and some mining operations.
Dampier port harbour master Vic Justice said the harbour had been cleared of boats but the port would be back in operation by the end of the week. Karratha's port had also been shut.
The Pilbara region is home to offshore oil and gas operations and mining operations, including iron ore, salt and nickel operations.
A spokeswoman for mining company BHP Billiton, Samantha Evans, said the company's iron ore and mining operations were proceeding as usual but shipments could not get out.