Celtic fought back from a three-goal deficit to snatch a share of the points in a dramatic match at Rugby Park.
First-half goals from Dean Shiels, Paul Heffernan and James Fowler had given the home side an emphatic half-time lead.
But Celtic fought back through two goals within three minutes from Anthony Stokes and a Charlie Mulgrew header with 10 minutes remaining.
Heffernan squandered a late chance for Kilmarnock to steal the points.
Neil Lennon had spoken of the need to make personnel changes after their loss to Hearts and dropped Badr El-Kaddouri, Victor Wanyama and Mohamed Bangura, with Cha Du-ri, Joe Ledley, Beram Kayal and Anthony Stokes coming in.
The home side also made four changes, with goalkeeper Cammy Bell not included in the squad because of an elbow injury and replaced with Anssi Jaakkola.
It was the home side who started more brightly, Celtic struggling to break down their impressive passing display.
But it was the visitors who had the first real chance of the match in the 12th minute.
James Forrest delivered the ball to Cha, who picked out the Irishman at the back post, Stokes unable to make any meaningful contact with the ball from just a yard out and sending the ball over the crossbar.
Kilmarnock continued to look the livelier side and their effort was rewarded in the 26th minute, Shiels' goal coming with the first shot on target by either side.
Right-back Alex Pursehouse sent an ambitious long ball that located Heffernan on the left wing, and his chip found the run of Shiels, who took a deft touch before driving the ball diagonally across goal and past Fraser Forster in the Celtic net from 12 yards out.
With Celtic clearly rattled, Kilmarnock continued to dominate, Liam Kelly almost increasing the lead in the 37th minute with a long-range shot from 40 yards out that forced Forster to tip the ball over the bar.
Paul Heffernan extended their lead just two minutes later, with Shiels the creator.
The Kilmarnock manager's son burst into space to evade Cha before slotting the ball through to Heffernan, who looked a touch offside as he drove home from inside the box.
Celtic then appeared to self-destruct as they lost a third goal. Mulgrew was at fault with a hapless pass-back to Forster that was pounced on by Fowler, who lobbed the ball over the goalkeeper.
That scoreline meant changes for Celtic in the second half, with Gary Hooper and Beram Kayal replaced by Wanyama and Bangura.
Their resurgence was signalled 10 minutes after the restart, with Forrest waltzing through the Kilmarnock defence. He was eventually dispossessed by Kelly, Pursehouse blocking a second attempt on goal.
With 69 minutes on the clock, Forrest again attempted to set up Stokes at the back post, the striker unable to match the pace of the ball and sending it behind for a goal kick.
However, he was given the opportunity to make amends when Kilmarnock conceded a free-kick 26 yards from goal, delivering a superb strike that gave Jaakola no chance.
Within three minutes, the game was reignited when Stokes grabbed a second. A right-footed strike from 22 yards out evaded the Kilmarnock keeper, who perhaps should have done better.
Kilmarnock's undoing was completed when Mulgrew headed home from close range with 10 minutes remaining to complete an incredible comeback that saw three goals in seven minutes.
The Rugby Park side had the chance to snatch victory when Heffernan contrived to head over the crossbar from four yards out with two minutes remaining of regulation time.