Hibs' offside trap frustrated the home fans and players in the first half as twice Peter Canero and once Gary McSwegan were denied by the linesman's flag when put through by man-of-the-match Stevie Fulton.
Fulton was the architect for Andy McLaren again 12 minutes after the re-start as he ghosted past his opponents to send the winger clear on goal, only to see the chance go by as McLaren pushed his shot past the far post.
The goal came in the 61st minute with another flowing move as Fulton fed Craig Dargo, whose cutback was perfect for McSwegan to volley home from 15 yards.
Mixu Paatelainen passed up a golden chance to equalise in the 67th minute following Jarkko Wiss' corner. A miscued clearance fell to the veteran six-yards out, but his snap-shot was inches wide.
John O'Neil missed an even better opportunity nine minutes later. He had time and space eight yards out after substitute Derek Townsley had unselfishly teed him up, but the midfielder pulled his shot well wide.
The leveller came in the 82nd minute when Craig James cross caught Gordon Marshall in two minds and allowed sub Paco Luna to power in a header off the underside of the bar.
Jamie Fowler almost put Killie back in front three minutes later but Nick Colgan stood up well to deny the youngster.
From the resultant corner however, Fulton was on hand to direct Fowler's chipped cross beyond the keeper into the bottom corner to give Killie a deserved victory.