By Agence France-Presse
Officials had warned of floods and landslides, evacuating thousands of people, but the storm weakened as it approached Taiwan and moved past it to the north.
Downpours of up to 100 millimetres (four inches) hit some areas overnight, according to the weather bureau, and strong winds were still expected as the storm moved northwest.
People were told to avoid the coast where waves as high as nine metres (30 feet) were recorded.
Television images showed trees felled overnight and blocking some roads in the mountains north of capital Taipei.
While official statistics did not record any fatalities, local media reports say a man fell to his death when he was checking the windows at his home.
Close to 3,500 people were evacuated across the island from areas prone to floods and landslides, with more than 2,000 soldiers mobilised.
About 43,000 households lost power at the typhoon's peak.
The storm also affected hundreds of flights.
Maria is the first typhoon of the season for Taiwan, and damage was limited for the island which is prone to violent storms through the summer.
Last year more than 100 people were injured when Typhoon Nesat battered the island, causing flooding and widespread power outages.