Power department officials said electricity network was disrupted as the storm uprooted trees snapping power lines in several areas.
Areas in South, East and North Delhi faced long power cuts ranging from one to four hours.
Several areas plunged into darkness immediately after the dust storm struck the city at 4:58 PM.
Supply of power could not be restored till late in the evening in several areas in North and North West Delhi.
"Power supply was affected in the entire city following the dust storm," said a senior official of the power department.