Jayden Stockley opened the scoring for the visitors before Izale McLeod levelled the game going into half-time.
Substitute Jake Taylor's low finish put Exeter back in front and Christian Ribeiro's neat header gave the visitors a two-goal cushion.
Ollie Watkins' cool finish punished slack County defending to seal the points for the Grecians.
Notts County's miserable home form continued as they were comprehensively beaten by mid-table Exeter.