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.
And as if to emphasise the paucity of the visitors' efforts, their almost anonymous debutant Adel Taarabt flipped a feeble free-kick into the Sunderland wall in the last act of what, from their point of view, had been a forgettable half.
But the visitors snatched their lead out of nowhere on 50 minutes when Duff floated in his set-piece from the left and Kasami rose highest to nod past Keiren Westwood - who had been rendered a virtual spectator until that point.
The goal shocked Sunderland back into action and they responded with a succession of near-misses, Johnson shovelling a shot wide, Duff picking the ball off Altidore's feet in the box and Sebastian Larsson plopping a poor free-kick into the Fulham wall.
And Sunderland spurned an even better chance in the 65th minute when Altidore was picked out by John O'Shea in the box and the striker swivelled past Aaron Hughes before firing just wide of Stekelenburg's right-hand post.
Stekelenburg denied Altidore at close range in the 75th minute but it was to be his last act of the game as he appeared to injure his shoulder in the process and was replaced by the visitors' substitute keeper David Stockdale.
Sunderland's attacking forays became more unfocused as time ticked by but substitute Ji Dong-won wasted a golden chance to equalise in the last minute of normal time when he headed wide.