Hibs were dominant for long periods but it was Scottish Communities League Cup winners Killie who emerged victorious as Shiels converted a 44th-minute penalty against the run of play after Jorge Claros was adjudged to have brought down Liam Kelly.
Leigh Griffiths, who scored the William Hill Scottish Cup semi-final winner to set up next month's all-Edinburgh final, was lively for Hibs, but Pat Fenlon's side now hold a six-point advantage over bottom club Dunfermline with four games to play.
The win saw Killie return to seventh place above Aberdeen and meant Hibs have one win and 10 losses at home this term and may yet require victory over Dunfermline, who yesterday drew 4-4 at St Mirren, on May 7 to avoid the drop.
A foot injury for striker Garry O'Connor could yet hamper Hibs' run-in, while Danny Racchi left the field on a stretcher for Killie midway through the second half.
Racchi was one of four changes for Killie, who included defender Ryan O'Leary for the first time since August following a knee injury.
O'Leary was immediately involved as Hibs made a lively start, making a well-timed tackle on O'Connor as the striker moved into the area.
A cross from Ivan Sproule was just too far in front of Isaiah Osbourne and Cameron Bell collected before Griffiths, who appeared full of confidence after scoring the winner against Aberdeen last weekend, attempted to go by Michael Nelson on the edge of the area but went to ground and was booked for diving by referee Craig Thomson.
Claros and Osbourne were beginning to get physical supremacy in midfield and Hibs' forwards were starting to benefit.
Griffiths was allowed space to shoot from 25 yards and forced Bell to turn the ball over the bar before an O'Connor header from a corner hit team-mate James McPake inside the six-yard box and the visitors scrambled clear.
O'Connor teed up Claros, whose shot from long range went just wide, before the striker found Griffiths after a hesitation by O'Leary, who recovered well to block as the Hibs man prepared to shoot.
McPake headed a Lewis Stevenson cross narrowly wide and Bell had to head clear after Griffiths attempted to latch on to a high ball forward from Claros, who then conceded a penalty.
Kelly was tripped in the box and Thomson had no hesitation in pointing to the spot, with Shiels converting to give the visitors the half-time lead against the run of play.
After Griffiths shot straight at Bell early in the second half, Hibs' hopes suffered a further blow with O'Connor departing and Roy O'Donovan coming on.
A Claros tackle midway inside the Killie half resulted in Racchi requiring lengthy medical attention and he was carried off with Lee Johnson replacing him.
An acrobatic O'Donovan effort was blocked before James Dayton mis-hit a clearance from a corner on to his own arm inside the area and the ball fell for Claros, whose effort was narrowly off target.
Bell held a 30-yard free-kick from Griffiths as Hibs again failed to find a way through.
Eoin Doyle replaced left-back Pa Kujabi as Hibs opted for a third forward and Bell had to be alert to punch clear a Paul Hanlon cross-cum-shot.
Substitute David Silva had an effort blocked by Matt Doherty after being played in by Shiels as Killie missed the chance for a second.
Five minutes of stoppage time followed but Hibs were unable to fashion a shooting opportunity and saw their three-match unbeaten run come to an end.
