The Irishman's right-footed effort was apt reward for a fine display by the home side during an opening period which also saw James McPake have a goal ruled out, while Tom Soares went close.
Kilmarnock enjoyed territorial dominance in the second half but Pat Fenlon's revamped Hibernian side defended superbly, with Paul Heffernan firing the visitors' best chance into the arms of the recalled Graham Stack.
The result is the Hibees' first home win since September, and first clean sheet in more than three months.
Fenlon handed debuts to two of their deadline day acquisitions, with Pa Kujabi slotting in at left-back and Matt Doherty coming in on the right side of a reshaped defence. Garry O'Connor and Stack also returned to the Hibees starting XI.
Gary Harkins was missing for Killie after suffering an ankle knock ahead of the encounter, which started with the home side making the running.
Tom Soares broke from a midfield melee with purpose and, from 25 yards, unleashed a fine strike which Scotland international Cammy Bell palmed wide in the fifth minute.
From the resulting David Wotherspoon corner McPake managed to nod into the net from close range, but referee Iain Brines adjudged that Bell had been impeded.
Hibs were displaying a vibrancy rarely seen at Easter Road in recent times, and deservedly claimed the lead after a quarter of an hour.
Some slick head-tennis on the edge of the box between Eoin Doyle and O'Connor managed to set Soares free on the right. The on-loan Stoke man's cut-back found Doyle and, although the Irishman fired his effort into the ground, the shot found the corner of the net.
Shiels' men emerged from their early slumber 10 minutes before the break when James Dayton showed excellent endeavour to dribble into the box and saw his low effort palmed away by Stack.
Paul Heffernan headed wide five minutes later from a Danny Racchi cross, while Liam Kelly shot over the bar.
Kilmarnock enjoyed territorial dominance in the second half but the Hibs backline, fantastically marshalled by captain McPake, remained utterly stoic throughout.
Fenlon's men could have doubled their lead on the counter-attack. Kujabi displayed some crowd-pleasing quick feet before slotting a fine through-ball to Doyle, but his low shot was saved by Bell.
A Racchi piledriver from the edge of the box tested Stack and that was followed by a James Fowler volley, which McPake threw his body in front of to block.
A blatant dive in the box on the hour mark by winger James Dayton was indicative of the Rugby Park side's desperation and frustration - yet inexplicably did not prompt a yellow card.
Kilmarnock finally created a truly clear opportunity with 10 minutes remaining. Liam Kelly finally cut through the solid Hibs defence with a fine pass, but Heffernan's low shot was well saved by Stack.
The former Arsenal youth was sharp again as the full-time whistle approached, pushing an awkward Racchi shot to safety - and a late onslaught was spectacularly foiled by a series of fantastic blocks by green jerseys.
