Vandals threw petrol at the front door of a home in Crawley and then set it alight.
The attack happened in Wayside, Ifield, at around 11.30pm on Monday (January 13).
A neighbour doused the flames with water before alerting the couple who live at the address.
DC Phil Peadon, of Sussex Police, said: “One of the terraced houses in Wayside, Ifield, was attacked shortly after 11.30pm on Monday but the fire was quickly extinguished by a neighbour.
“I would ask anyone who saw anyone acting suspiciously in the area that evening or has information in relation to the incident to contact police on 101 quoting serial 1459 13/1 or the independent charity Crimestoppers anonymously on 08000 555 111.”