The Argentinian snatched victory with a header in the second minute of injury time at the end of extra-time just as it looked as though a compelling tie was heading for penalties.
Newcastle led three times through Peter Lovenkrands' double and Danny Simpson's fluke strike, but equalisers from Robbie Findley, Matt Derbyshire and, in the 115th minute, Marcus Tudgay, kept the result in doubt until Coloccini's late, late intervention.
Manager Alan Pardew, who rested nine of his first-teamers, will have been delighted to leave the City Ground with the club's name in the hat, but there were plenty of positives too for beleaguered Forest counterpart Steve McClaren as his side pushed their Barclays Premier League opponents all the way.
Pardew admitted before the game that he would make changes as he attempted to protect the men who have left the club sitting in fourth place in the top-flight table after an unbeaten start to the campaign.
His decision to rest so many - only Coloccini and Simpson were retained from the starting line-up at Aston Villa on Saturday - handed chances to a series of under-studies, but perhaps more importantly, the long-suffering Hatem Ben Arfa.
The Frenchman had managed only four competitive appearances for the club before running out at the City Ground almost 12 months after suffering an horrific double leg fracture, with his return delayed by an ankle ligament injury picked up in pre-season.
There were debuts too for keeper Rob Elliot and 19-year-old midfielder Mehdi Abeid as Pardew gave his fringe players their heads.
Abeid was impressively tidy in central midfield as he and Danny Guthrie attempted to start the creative process.
However, it was another Frenchman, Sylvain Marveaux, who proved the first half's pivotal character.
He might have given the Magpies a 12th-minute lead after being played in over the top by Danny Guthrie's delicious pass, although he delayed fatally to allow full-back Brendan Moloney to cover across and make a vital block.
But as the half wore on, Marveaux began to prosper down the Newcastle left, and when his big moment came, he did not disappoint.
There were six minutes of the half remaining when he received the ball close to touchline and after looking up, delivered the perfect cross into the box.
Lovenkrands could hardly have asked for a better ball and did it justice with an unstoppable close-range header to leave Camp helpless.
Forest, who were still coming to terms with Saturday's unpalatable home defeat by Derby, gave as good as they got for long periods of the opening 45 minutes, but Elliot did not have a single save of note to make.
Pardew may well have urged caution at the break, but if he did, his message went unheeded as Forest dragged themselves back into the tie in some style.
There was less than a minute of the second period on the clock when Findley was allowed to make ground towards the Newcastle penalty area before unleashing a stinging right-foot shot which flew past the astonished Elliot's despairing dive and into the bottom corner.
Newcastle responded immediately and might have restored their lead within seven minutes when Ben Arfa chose his moment to show what he could do.
The Frenchman picked up possession in midfield and a burst of pace took him past Chris Gunter before he picked out Lovenkrands' run into the box, only for the striker to shoot straight at Camp.
But the Premier League outfit were back in front on the hour with Marveaux once again the man providing the ammunition.
His run into the box prompted Moloney to haul him back, and referee Lee Mason had little hesitation in pointing to the spot to allow Lovenkrands to double his tally.
But Forest were far from finished and they were back on terms for a second time within seven minutes when Derbyshire got in behind the Magpies' rearguard and rounded Elliot with ease to slide the ball into an empty net.
The Ameobi brothers, Shola and Sammy - the older man was spoken to after a pushing match with defender Joel Lynch - and Gabriel Obertan were all introduced as Pardew looked to avoid extra-time.
But despite a late flurry during which Findley blasted across the face of goal, the additional 30 minutes were required.
Simpson's 93rd-minute cross, which floated over Camp and into the back of the net, looked to have won it for the visitors, but Tudgay struck with five minutes of extra-time to go when he tapped home substitute Ishmael Miller's cross from close range.
There were literally seconds to play when Obertan fired the ball in once again from the left, and Coloccini arrived perfectly on cue to finally dash Forest's hopes.