Goals in each half from Filipe Morais and Steven Fletcher were enough to give them the three points.
Killie took the game to Hibs and there was an early chance for Danny Invincibile after good work by David Fernandez, but the angle was too tight and he could only divert the ball past.
But Merouane Zemmama cheered the home fans with a brilliant run from deep inside his own half. He flicked the ball over Garry Hay and then beat Craig Bryson for pace, before picking out Morais at the back post but his header could not find Fletcher.
At least it gave Hibs some respite after they had spent most of the first ten minutes with their backs to the wall.
Morais was then not far away from connecting with a long through ball from John Rankin as Hibs looked to spark something, but chances were few and far between and the flow of the game was not helped by a series of niggling fouls.
Charlie Richmond did not help with a number of curious decisions, not least of which was to award Hibs a corner midway through the first half after Martin Canning clearly ran the ball out of play.
Zemmama looked the one player capable of making the breakthrough with his darting runs and willingness to try something different.
It was Hibs that made the breakthrough with a route-one goal after 29 minutes. Rob Jones played a long ball up to Colin Nish who nodded the ball down for Morais to take it in his stride.
There was still some work to do, but he raced in on goal before placing the ball beyond Alan Combe from just inside the area.
Hibs wasted a decent chance to extend their lead when Jamie Hamill was penalised for a passing the ball back to Combe. Fletcher played the indirect free-kick to Zemmama but, instead of shooting, he tried to dribble his way in and was crowded out.
Invincibile should have equalised early in the second half, but he sent his six-yard header wide with Hibs leaving him unguarded.
Hibs had the better of the second half and it took a superb save from Combe to keep out a volley from Zemmama.
The goalkeeper distinguished himself again when he blocked a Fletcher shot when the Hibs striker got clear of the Killie defence.
But Kilmarnock did not heed the warning and Fletcher wrapped up the points with a crisply-struck left-foot shot after 73 minutes, after again out-sprinting the defence.