The Toffees fell behind when Gaston Ramirez opened his Saints account in the sixth minute with a back post header from a corner before Leon Osman fired home from close range after Southampton defender Jose Fonte failed to clear Kevin Mirallas’ dangerous cross.
Just after the half-hour mark, Nikica Jelavic made it 2-1 with a delightful finish on his left foot from the left side of the area before he added a second in the 38th minute with a header to send Everton on their way.
Goodison Park, Liverpool
Yellow cards: EVE - nil
SOU - nil