Defeat was tough for the Black Cats fans who had witnessed a second-half onslaught on the Everton goal with only a stunning save from goalkeeper Nigel Martyn denying substitute Anthony Le Tallec.
But Sunderland's overall lack of the killer instinct in front of goal proved to be their downfall again and relegation looms closer by the match with time fast running out for manager Mick McCarthy.
He suffered a pre-match blow when midfielder Christian Bassila pulled out with a recurrence of a hamstring injury, Tommy Miller taking over.
Everton were without the suspended Phil Neville and Mikel Arteta, sent off in the Boxing Day Merseyside derby defeat by Liverpool, James McFadden and Cahill returning to the starting line-up.
With the teams conceding 65 Premiership goals between them this season, goalscoring chances were expected to come thick and fast in the bitter battle to avoid relegation.
But poor passing by two very ordinary sides gave the fans little festive cheer with McCarthy running out of patience by the 40th minute, hauling off the ineffective Andy Gray in favour of Le Tallec.
The home relied heavily on the running power of Jonathan Stead, who should have finally broken his goalscoring duck for the Black Cats, only to shoot straight at Martyn when sent clear in the 30th minute.
A quickly-taken free kick by Stead in the opening minutes was latched on to by Liam Lawrence whose low cross was scrambled away by David Weir.
But Everton responded through Leon Osman whose low drive almost deceived Kelvin Davis, the goalkeeper reacting late to a low drive that was scrambled behind for a corner, Davis again failing to deal confidently with the flag-kick and lucky not to concede.
Lawrence had a low drive well saved and Miller just failed to get on to the end a Stead centre that was hooked clear by Weir, but Everton always looked more dangerous in attack.
Gary Breen just beat James Beattie to a Cahill cross and a low drive from Kevin Kilbane, booed throughout his return to the Stadium of Light, brought a smart save from Davis.
Breen was cautioned for a cynical trip on Kilbane, a fifth yellow card of the season which rules him out of Monday's match at Fulham, but referee Rob Styles kept the bookings to a minimum.
Julio Arca set the tone for Sunderland's second-half dominance, Nuno Valente clearing a low drive off the line then Stead crossing to find the head of Le Tallec only for Martyn to turn the 52nd minute effort behind with a one-handed save.
Lawrence sent a fierce drive inches past the post then Miller failed to direct a free header on target from the resulting corner.
Everton manager David Moyes, who had sent on Marcus Bent for the start of the second half, obviously felt the game was there to be won when he introduced Duncan Ferguson in the 67th minute to form a three-pronged attack.
But it was Sunderland who went all-out for the winner only to be sickened by the old sucker punch deep in time added on.
Kilbane's right-wing corner was met by Cahill who thundered a header high into the net to the delight of the Everton fans behind the goal.