The home side had lost four league games on the trot and it seemed that the tide had finally turned when first half substitute Garry Hay volleyed in a superb opener in the 68th minute.
But late pressure by the visitors eventually paid off when a David Zitelli (pictured) corner was met powerfully by Laursen and with Gordon Marshall in no-man's land the ball thudded in off the bar.
Marshall had earlier distinguished himself with a flying save from a Zitelli free-kick and Hibs will feel like they deserved a penalty just before Killie took the lead.
Lyndon Andrews, the Trinidad and Tobagan star had jinked into the box in the 65th minute and was brought down just on the edge of it.
Replays showed that a penalty was the correct decision but referee Mike McCurrick were only rewarded with a free-kick on the edge of the box, Zitelli curled it around the wall but Marshall flew to his right to palm it away.
It took some time for the game to come to life, as the best defensive record in Hibs went head-to-head with the worst goalscoring record in the top six.
On the half hour Martin Baker got on the end of a free kick from the left but his header was saved low down by Nicky Colgan.
Hibs had the ball in the net in the 36th minute after Mixu Paataleinen had headed the ball back and Mark Dempsie finished well but was given offside.
French defender Franck Sauzee looked composed throughout the game but almost embarassed himself five minute before the break when he allowed the ball to bounce over him, Craig Dargo nipped in in front of Sauzee and looked odds on to score but skied the ball over the bar from just six yards.
It took until the 57th minute for the first booking and Dirk Lehmann received it for pulling over Gus McPherson.
Dargo it was who set up Hay's goal but Hibs had plenty of chances to draw level.
Zitelli fired a 76th minute free-kick wide but the turning point of the game occurred with ten minutes to go.
Dargo burst onto the ball and fired goalwards, Colgan only got a hand to it and palmed it onto the bar, from which the defence cleared.
Stung into action, Russell Latapy, a constant thorn in Killie's side should have made it 1-1 a minute later when he brilliantly beat three men in the box but with a clear shot at goal he somehow dragged it wide.
After Laursen's header, Latapy had a chance to equalise but after a good run down the left, he cut inside and saw his low shot just go wide with Marshall beaten.
