Killie had the first chance of the match within a minute of the kick-off when David Fernandez nodded the ball down to Mehdi Taouil whose swerving shot was parried out by Yves Makaba-Makalamby in the Hibernian goal.
Killie skipper Garry Hay also went close in the fourth minute with a powerful shot free-kick which shaved the crossbar.
Killie's good start was nullified and Hibernian's midfield gained control of the game, but the final pass let them down on numerous occasions when in promising positions.
Moroccan Merouane Zemmamma's was typical of Hibs' general performance with many pieces of skill and artistry, but with wasteful shooting.
Kilmarnock took the lead in the 36th minute against the run of play with a well worked goal.
Gary Wales fed Jamie Hamill wide on the right and he measured a cross to the near post where Colin Nish completed a 60-yard dash to stoop and guide the ball home off both posts.
Hibs crafted their clearest opening a minute later when half-time substitute Dean Shiels slid a tempting-looking ball across the face of goal, but it didn't seem to interest Ross Chisholm who failed to anticipate and the chance was lost.
Killie's own Moroccan, Taouil, showed a flash of his skill with an acrobatic scissor kick which was on target but lacked the power to beat Makaba-Makalamby.
Craig Bryson was next to threaten in a good Killie spell with a great burst from midfield in the 74th minute, but his shot flashed narrowly past.
Killie did stretch their lead a minute later after Nish showed good composure on the byline before delivering a chipped ball to the far post where Taouil volleyed home.
Hibs should have been back in the match straight from kick-off but Chisholm skewed the ball wide from six yards.
They had an even better chance to get back into the match in the 89th minute when Killie conceded their 13th penalty of the season when Alan Combe spilled an innocuous ball and Hamiil blocked Shiels' attempt to gather.
Shiels made no mistake from the spot, but it was no more than consolation for the Edinburgh side.