Sammy Clingan gave Killie the lead just after the break with a long-range strike, but Ryan McGivern levelled five minutes from time.
The visitors looked to have grabbed the points when Jude Winchester netted.
But ace striker Leigh Griffiths earned Hibs a point with a third goal in as many minutes.
If the opening 45 minutes was dull, the second half was the complete opposite.
Clingan came the closest in the opening 45 minutes, hitting a post from 25 yards.
The hosts ignored the warning and were made to pay less than a minute into the second half.
Northern Ireland international Clingan picked the ball up 30 yards from goal and skipped a challenge before scoring with a great, swerving strike.
James Dayton and Winchester both went close soon after as Hibs looked to be on the verge of collapse.
Then Rory McKeown gathered from Clingan. He lobbed the ball over the advancing Paul Cairney then twisted his body sideways to connect on the half-volley and send the ball crashing back off the far post.
Then came the late goal flurry.
McGivern rose high to power a header into the far corner.
But Hibs' celebrations were muted when they went 2-1 down.
William Gros found Winchester with a pass and the youngster curled an inch-perfect effort that rested in the back of the net off a post.
However, Hibs levelled for a second time, with Griffiths on hand to flick home a pass from Eoin Doyle.