The Ayrshire side recovered from a red card to goalkeeper Alan Combe and the loss of two penalty goals late in the first half to secure an unlikely victory.
Killie could hardly have wished for a better start and took the lead after just five minutes.
Danny Invincibile crept in unnoticed at the back post to get on the end of a Jamie Hamill cross and steer a volley into the roof of the net.
Hibs hit back and Sol Bamba had a shooting chance from the edge of the area but thumped it high and wide.
But Kilmarnock dominated the early play and Hamill delivered another dangerous ball across the face of the goal which Rob Jones managed to hook for a corner.
Hibs then failed to clear Mehdi Taouil's flag-kick and when the ball broke to Allan Russell on the edge of the box, he cracked the ball high into the net with the aid of a deflection.
Hibs lost the services of skipper Rob Jones after 28 minutes when he limped off to be replaced by Steven Thicot.
But Hibs found a way back into the game ten minutes from the break.
Dean Shiels showed some clever footwork in the box and fell to the ground after a challenge from David Fernandez.
Referee Norris pointed to the spot much to Kilmarnock's fury but Shiels stepped up to send Combe the wrong way from the penalty.
Incredibly, Hibs had their second penalty two minutes later when Colin Nish was upended by Combe as he went past him in what was a more clear-cut decision.
This time, Combe was red carded for denying Nish a goal and it was fully three minutes before Mr Norris completed the paperwork and Shiels beat substitute goalkeeper Damien Rascle with his second penalty.
But Killie were back in front two minutes after the break when Invincibile headed in a cross from substitute Willie Gibson.
Hibs sent on Derek Riordan to try and salvage something, but it was Kilmarnock who went further ahead 15 minutes from time.
Thicot put Bamba in trouble with a poor pass and Gibson raced up field to release Garry Hay, who beat Yves Makaba-Makalamby from an acute angle.
There was no way back for Hibs after that as Killie held on for a valuable three points.