At one stage more than 2,500 customers in the Milford area were without power.
Hundreds more customers in Rathmullan, Ramelton, Ray, Kilmacrennan, Keadue, Burtonport, Dungloe and Arranmore Island were also cut off.
As of midnight, just 16 homes in Milford were still affected.
ESB has apologised for the “inconvenience” of the outages which were weather related.
“The power cuts were caused by extremely high winds on Saturday evening and crews worked into the night to restore power to customers,” said an ESB spokeswoman.
The horrible Saturday weather saw wind gusts of 110 km/hr, slightly less than forecast but still extremely strong.
It also brought torrential rain which is continuing overnight; the N56 between Creeslough and Dunfanaghy was flooded for a time.
Gardaí are warning motorists to take extra care on the roads on Sunday morning.
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