The pilot and one passenger, both of whom were seriously injured, have now been rescued after the power lines were deactivated.
The incident caused chaos in parts of Maryland state, knocking out the power supply to hospitals and schools.
About 120,000 people were left without electricity across the state, the Pepco Utility company, which operates in the Washington area, told CNN. Power was restored on Monday morning, authorities said.
The aircraft, a Mooney M20J propeller plane with a capacity of four, hit the power lines in fog, authorities said. It had been flying from New York to an airfield in Montgomery Village, Maryland.
Montgomery County Fire and Rescue Service Chief, Scott Goldstein, said both men were suffering from hypothermia after being rescued in a complex operation that involved ensuring the plane did not fall from its precarious position before the injured pair could be brought down safely.
He said two local hospitals were forced to operate at a limited capacity, after temporarily losing power.