Trailing to Gary Wales' first-half strike, Derek Riordan and substitute Paul Dalglish turned the game on its head with their late counters.
Riordan went close early on for Hibs with an inswinging corner which Alan Combe did well to flip over his crossbar.
Steven Whittaker then dragged an 18-yard shot wide after the lively Riordan had again created the opening.
But it was Kilmarnock that took the lead after 19 minutes. A long clearance from Combe was held up by Colin Nish who then fed Wales and he clipped a neat finish past Zibi Malkowski.
Hibs hit back and, four minutes later, Abdessalam Benjelloun, making his SPL debut, cracked in a brilliant shot which brought the best out of Combe.
But Kilmarnock were more accurate with their shooting and Malkowski had to be on his toes to clutch a Nish header at his right-hand post.
The Polish goalkeeper then had to leap to his left to push a Wales shot away for a corner.
Hibs came within inches of an equaliser four minutes before the break when Benjelloun found Steven Fletcher in the area and his shot beat Combe but cleared the far post.
Fletcher should have done better early in the second half when he took a Whittaker pass in his stride but lofted his shot well over the top.
Riordan did force Combe to save after 62 minutes but his 20-yard effort was straight down the throat of the goalkeeper.
Chris Hogg then headed over from just six yards from a Kevin Thomson free-kick as Hibs went for the equaliser.
It came ten minutes from time when Lindsay Wilson could only push a Thomson pass into the path of Riordan who steadied himself before thumping his shot into the roof of the net.
Then came Dalglish's late winner after Gary Caldwell had supplied him with just four minutes left and he cracked the ball home off the underside of the bar.