Swiss youth international Kasami converted the simplest of chances to score his first goal since joining the Cottagers in 2011, rising at the far post to nod in a corner from Damien Duff.
It was Fulham's only real chance of a game which the home side had dominated, with a number of the five new Di Canio signings on show coming close to breaking the deadlock in the first period.
Cape Verde international Cabral looked most impressive, drilling two long-range shots wide, while right-back Ondrej Celustka hit a rising half-volley which was tipped over by Fulham goalkeeper Maarten Stekelenburg.
But for all their first-half fluency the Black Cats clearly lacked some cutting edge and they faded in the second period as Martin Jol's men, marshalled superbly by captain Brede Hangeland in the centre of defence, hung on for victory.
Cabral, a talismanic influence in the middle for the home side, hit an early chance wide before Fulham's hopes were hit by the loss of former Sunderland defender Kieran Richardson due to injury with just 19 minutes on the clock.
Richardson's exit seemed to sentence Fulham to even deeper defending as they were pinned back for long periods by the pace of Adam Johnson and Italian Emanuele Giaccherini down the flanks.
But if front men Stephane Sessegnon and Jozy Altidore - fresh from a midweek hat-trick for the United States - lacked a little cutting edge up front, the same could not be said for Cabral, who hammered another long-range effort narrowly wide after 27 minutes.
Giaccherini, lively but occasionally lost on the left, drifted in-field to pick up a pass from Johnson and hit a hard left-foot effort straight at new Fulham keeper Stekelenburg just past the half-hour.
And the quietly efficient Celustka came close to turning up the volume two minutes later when he unleashed a rising half-volley from 25 yards which Stekelenburg had to stretch to tip over the bar.
Source: PA
Source: PA