Playing just over 24 hours after Malky Mackay was sacked, Cardiff dominated the opening hour with Jordon Mutch and Fraizer Campbell putting them two goals ahead.
But Sunderland, who were dreadful for the first 45 minutes, rallied late through a Steven Fletcher toe-poke, before substitute Colback's deflected effort beat David Marshall in the fourth of five added minutes to level matters at the final whistle.
The sacking of Mackay has been widely condemned and ensured the spotlight was firmly on the home side, but there were no signs of any genuine venom being directed towards owner Vincent Tan, although there were several pro-Mackay chants and banners in evidence throughout the game.
With the Scot's lieutenants David Kerslake and Joe McBride in charge, the Bluebirds players seemed bent on taking out their frustrations at the loss of their popular boss on a Sunderland side who paid for an awful start.
Inside a minute Mutch had surged into the box and gone down as Valentin Roberge closed in, although the midfielder was booked for diving as the Sunderland defender withdrew his foot.
The former Birmingham man should have given the hosts the lead in the third minute, but could not keep his header down from a Craig Noone cross after Kim Bo-kyung beat compatriot Ki Sung-yueng to the ball in midfield.
But Mutch made no mistake in the sixth minute. Roberge was robbed by Campbell and Mutch drove forward to drive the ball beyond Vito Mannone with the help of a deflection off Modibo Diakite.
"That one's for Malky", chanted the home support, and the chances kept coming.
Mannone tipped a fizzing Kim strike over the bar, while Steven Caulker headed straight at the goalkeeper from close range.
Campbell sent a low diving header a few yards wide from a teasing Noone centre, and Peter Whittingham attempted to pull a ball back across goal when he should have shot inside the six-yard box.
Sunderland slowly found a foothold in the game and they could have been level after half an hour but for a horrendous miss by Jozy Altidore.
David Marshall pushed away a Kim strike and all the Black Cats striker had to do was tap home, but he sliced wide.
Marshall, one of the stars of Cardiff's season, then made two superb saves from Fabio Borini as the visitors finished the half strongly.
Gus Poyet sent on Fletcher for Borini at the break but they remained on the back foot and fell further behind in the 58th minute.
Mutch was given far too much room down the left by three Sunderland defenders, and Campbell finished with ease at the far post. Tan marked the goal by performing the club's 'Ayatollah' celebration.
Lee Cattermole fired narrowly over from Sebastian Larsson's corner at the other end.
The life had gone out of the game but Fletcher earned Sunderland a lifeline when he tapped in at the far post from Emanuele Giaccherini's cross.
It sparked a late onslaught, and Cardiff looked set to hold out until Colback struck to spark delirium in the Sunderland ranks, although the Black Cats remain rooted to the foot of the table.