Thurrock, managed by Robbie Garvey, brought a strong team to Mill Field on Thursday and although the Millers put in a good performance, their Blue Square South opponents proved too good.
Goals from Paul Terry, Joe Bruce and Dee Okojie was enough to pick up the win for Fleet.
Aveley: McCartney, Wilson, Read, Russell, Ngakam, Slatter, Bonnett-Johnson, Hyde, Stanley, Ali, May, Dove, Marfo, Parmenter, Robson, Hause, Harrison, Fabiani, Dady, Springett.