Nish took advantage of some sloppy defending to head home in the 49th minute and Combe pulled off some excellent saves as Killie vigorously defended their lead.
Combe endured embarrassment last week when his throw-out hit Darren Mackie's head and landed in the back of his net at Aberdeen but he more than made up for that freak goal.
Hibernian dominated possession in the first half with young midfield trio Lewis Stevenson, Kevin McCann and Ross Chisholm comfortable on the ball. But Rob Jones, back from injury along with David Murphy, failed to deal with a simple long ball to allow Nish to score.
And Killie, who blooded Willie Gibson, Ryan O'Leary and Jamie Hamill, held on with some stout defending.
The game had an initial feel of an end-of-season contest but Benjelloun sparked it to life in the 19th minute when he took a long ball brilliantly on his chest, cut inside left-back Frazer Wright and smashed a powerful shot that Combe pushed past his near post.
Killie were playing five men in midfield but that included attack-minded players Steven Naismith, Gibson and Gary Wales.
And Naismith reminded Hibs of his danger when he burst forward midway through the half and unleashed a superb 25-yard strike that Andy McNeil pushed over his bar.
Hibs stepped up a gear and twice came close from two Murphy corners in the space of a minute.
Hamill diverted Chris Hogg's 18-yard strike over the bar before Combe beat away a far-post header from Jones.
Combe then pulled off an incredible triple save from Shiels after a great through ball from Steven Fletcher, with Frazer Wright turning the ball on to his own post after the first parry from his goalkeeper.
Hibs looked to be turning the screw and Benjelloun played the ball across the box to set up overlapping right-back Steven Whittaker, but he sliced wide.
However, Killie almost snatched the lead in the dying seconds of the half when Gibson worked space in the box after a one-two with Nish, only for McNeil to stop his low shot. The brilliant Combe even had an assist to look back on when Jones failed to deal with hiss massive kick-out under pressure from Nish, and the Killie striker nodded the ball over the stranded McNeil.
Hibs boss John Collins brought on winger Ivan Sproule for McCann and Jim Jefferies immediately responded with Sylla on for Gibson.
Some committed defending kept Hibs at bay as the home side threw the ball into the box.
Killie - with Wright moved to central defence in a swap with O'Leary - deprived Hibs of any space to work an opening.
Shiels managed to weave his way through but Combe held on to his shot from a tight angle and the keeper then turned the Northern Irishman's 20-yard drive past the post.
And the Killie keeper's stunning one-handed save a minute later stopped Hogg converting sub Merouane Zemmama's corner.
Jones almost gifted Killie a second when he fluffed a clearance straight to Gary Wales but Zemmama cleared his deflected effort off the line. Hibs stepped up their search for an equaliser but James Fowler blocked brilliantly from Shiels from close range and Fletcher's 25-yard chip just cleared the back post.
And Combe saved from Sproule in injury time with the Northern Irishman clean through before Fletcher skied the rebound.