The Hoops looked down and out as Killie raced to an astonishing interval lead through Dean Shiels, Paul Heffernan and James Fowler.
However, the second half, if anything, was even more dramatic. Celtic striker Anthony Stokes scored twice in three minutes, the first from a free-kick in the 73rd minute, before stand-in skipper Charlie Mulgrew headed an equaliser from close range and save the visitors' blushes.
Manager Neil Lennon would have settled for the point at half-time when his side were booed off the park but when the excitement dies down he will realise another two SPL points were dropped.
Killie might have sneaked it at the end but Heffernan missed the target from just a few yards out, but the home fans were simply glad they did not go home with nothing from a great afternoon's entertainment.
Once again Lennon rung the changes, although one was enforced by the suspension of midfielder Kris Commons after being sent off in the last outing at Hearts.
Badr El-Kaddouri, Victor Wanyama and Mohamed Bangura all dropped to the bench, with Cha Du-ri, Joe Ledley, Beram Kayal and Stokes coming in.
Kenny Shiels' Killie team also showed four changes with injured keeper Cameron Bell replaced by Anssi Jaakkola and Danny Buijs, Gary Harkins and Liam Kelly coming in for Zdenek Kroca, Gary Fisher and James Dayton, who were all among the substitutes.
With Stokes back alongside Gary Hooper in what many feel is the Parkhead side's most potent strike force, Celtic fans were confident but they might have guessed at the horror which was to unfold in the first half when the Irishman missed a sitter after 12 minutes.
Right-back Cha galloped on to a perfectly-weighted James Forrest pass and cut the ball across the six-yard box only to see Stokes miss the target with the goal wide open.
But in truth, that incident did not hint at what was to come.
The game was stretched and open but there was still some surprise when Killie took the lead in the 26th minute through Shiels with an opener which owed much to route-one football.
Right-back Alex Pursehouse drove a long diagonal pass for Heffernan to chase into the Celtic box and he turned inside Hoops defender Daniel Majstorovic to set up the former Hibernian player, whose first touch gave him the space to drive low past Forster from 12 yards.
Celtic looked all over the place for the next few minutes and Forster had to dive low to his left to smother a Fowler drive after the visitors had been caught on the break.
In the 37th minute, in yet another Killie break, Forster had to fly high to his right to tip a long-range drive from Kelly over the bar for a corner, which came to nothing.
Five minutes from the break there was more drama when Shiels fired in a cross from wide on the left and Heffernan nipped in behind the static Parkhead defence to guide the ball past Forster from close range.
The Parkhead side were in disarray and in the final seconds of the half the strong-running Fowler raced on to a short headed back-pass from Mulgrew to lob the ball over Forster for number three.
It was a stunned Rugby Park who tried during the interval to digest what they had just witnessed in the first 45 minutes.
Lennon replaced Hooper, who appeared to have taken a knock, with Bangura while Wanyama came on for the excitable Kayal, who had picked up a booking and was treading on thin ice.
The home fans, nervous despite such a commanding lead, awaited a Celtic backlash but while there was a predictable determination from the visitors they were still leaving gaps at the back.
Celtic, though, kept pushing for the goal which they hoped would spark a comeback and Jaakkola made a decent save from Cha's angled drive before Kaddouri came on for Cha.
And in the 73rd minute, after Killie defender Mo Sissoko was booked for a foul on Forrest 25 yards from goal, Stokes hammered the free-kick high past Jaakkola to give the Hoops the lifeline they needed.
Three minutes later, as the visitors piled on the pressure, Stokes turned and fired a low drive from 30 yards past Jaakkola for his second - and there was more drama soon to follow.
In the 79th minute Mulgrew made up for his first-half error when he headed in the equaliser from a yard out after Majstorovic had knocked a long free-kick from Ki back across the goal.
The final moments could not have been more tense and with two minutes remaining Heffernan missed a sitter with his head after he had been set up by Harkins six yards out, the Killie striker lifting the ball over the bar.
