Members of the Rail, Maritime and Transport union backed walkouts and other forms of industrial action by 9-1.
The union has accused operator Serco of failing to fix faults on the service between Scotland and London.
RMT general secretary Mick Cash said: “The poor service to passengers, in conjunction with the company’s failure to address the issues raised by RMT representatives and officials in recent talks, reached the point where the union decided enough is enough and left us with no option but to ballot for industrial action before someone is injured.
“That ballot has now recorded a massive vote for action and that mandate will be considered by the union’s executive.
“The sleeper franchise was awarded to Serco by the Scottish Government and the multinational privateer took over from First Group on March 31 this year. Our members have been unhappy with Serco’s management of the iconic service from Scotland to London since the very early days of them taking on this 15-year franchise.
“This is yet another example of Serco winning public sector contracts and failing to deliver for the taxpayer, passengers and staff.”
The union claimed there were more than 200 defects on trains, including smoke detectors disconnected, toilets being inoperable, and lighting and heating systems not working.
Air conditioning problems throughout the summer left passengers sweltering in the sleeping berths, said the RMT, adding there was no hot water in some coaches for hand washing.
Officials claim there has been a loss of power in coaches during some journeys, leaving staff having to find alternative accommodation during the night for passengers.