Terry Butcher's men had to come from behind to draw 1-1 after Rory McKenzie had given Kilmarnock a first half lead.
But after Danny Haynes grabbed the equaliser early in the second half the Easter Road side had plenty of chances to claim their third win of the season over the Rugby Park side.
In the knowledge that a win would move them into sixth place, Hibs had most of the early pressure.
Their first shot on target came after four minutes when Sam Stanton's free-kick was cleared only as far asAlex Harris, whose drive was at a good height for Craig Samson to make a comfortable save.
After 10 minutes a floated free-kick from Harris found Michael Nelson but from eight yards out his header bounced wide of goal.
Kilmarnock offered little goal threat until the 18th minute when they snatched the lead with a brilliant goal.
Alexei Eremenko, making his first home start since he returned to the club, slipped the ball to Kris Boyd who immediately sent a 50-yard pass in behind Ryan McGivern for Rory McKenzie.
The Killie midfielder had a lot to do but drilled an angled drive from just inside the box beyond Ben Williams and into the corner of the net for a finish to match Boyd's superb pass.
Hibs replied immediately with a low drive from Danny Handling but again it was an easy save for Samson.
From a similar position at the other end Craig Slater tried likewise but screwed his shot well off target.
Goalmouth action was limited for the remainder of the first half, although on loan striker Haynes curled a shot wide.
The home side replaced Robbie Muirhead with Greg Kiltie at half-time but it was Hibs who continued to force the play at the start of the second half.
And after the Killie defence failed to clear its lines, Tom Taiwo curled a 20-yard effort just beyond Samson's left hand post.
The Edinburgh side were rewarded with an equaliser after 57 minutes. Stanton whipped in a low cross from the right and Haynes stooped to powerfully head the ball past Samson from eight yards.
Two minutes later the Hibs pair were at the centre of the action again. Jeroen Tesselaar tripped Haynes just outside the 'D' - allowing Stanton to curl a free-kick over the wall and narrowly over the crossbar as the visitors chased a winner.
With 20 minutes remaining Hibs brought on captain Liam Craig, before a rare Killie attack saw Mark O'Hara's left-foot drive go over.
Taiwo was then allowed to run at the home defence but his firm drive from 22 yards was straight at the 'keeper.
As both sides chased a winner in the closing stages Boyd had a chance to grab all three points but his poor first touch from Michael Gardyne's floated pass allowed the ball to roll harmlessly towards Williams.
It took a great block from Manuel Pascali inside the six-yard box to keep out a Haynes snapshot.
With three minutes remaining Hibs sent on leading scorer James Collins for Haynes - but Stanton came closest to a late winner when his shot was charged down by Boyd.