Following a rain delayed start, an opening stand of 88 from Hamish Marshall (37) and captain Michael Klinger (83) set Gloucestershire on their way to an 185-4 innings.
Sussex struggled to 49-3 early on, losing opening batsman Chris Nash to a L.B.W. from a James Fuller delivery after just three balls.
However, a late rally led by the irrepressible Wright (111 n.o.), saw Sussex claim the victory with just one ball left as the visitors finished with 188-7.