The visitors lost their first league goal of the season when Conor Sammon gave Killie the lead after only seven minutes but just before the break, Stokes, on for the injured Paddy McCourt, was brought down by Frazer Wright and Daryl Murphy netted the penalty.
Former Hibernian striker Stokes converted an Emilio Izaguirre cross from close range in the 51st minute and the Parkhead men looked comfortable for the rest of the second half giving Neil Lennon his 13 straight SPL win in succession to his credit since becoming Celtic manager.
A clean sheet victory for the visitors would have seen them record their best start to a domestic campaign since 1906 – five wins without losing a goal.
But it took only seven minutes for that statistic to disappear. Alexei Eremenko’s clever pass sent Killie’s lone-striker Sammon through on goal and the Irishman lost Celtic stopper Glenn Loovens before slotting low past Hoops’ keeper Fraser Forster for a dramatic if unexpected opener.
The visitors pushed hard for the equaliser but in a 15th minute breakaway, Kilmarnock midfielder Jamie Hammill sent skipper Craig Bryson clear of the Hoops’ defence but Forster won the race to the ball at the edge of the box.
But the rest of the half was controlled by the visitors with McCourt, who had returned at the expense of injured James Forrest, looking the biggest threat to Killie with his mazy runs.
However, in the 21st minute the former Derry City player landed awkwardly on the bye-line following a tussle with Eremenko, appearing to injure his shoulder, and had to be replaced by Stokes.
Nevertheless, Celtic’s corner count increased as the pressure intensified but they could not fashion even a half-chance to test Killie goalkeeper Cameron Bell.
However, in the 40th minute, after another period of intense pressure, Rugby Park defender Wright clumsily brought Stokes down in the box to concede a penalty.
Murphy sent Bell the wrong way from the spot to deservedly level the scores – albeit from Celtic’s first direct shot at goal.
Moments from the break, Parkhead defender Cha Du-Ri’s deflected cross from the right-hand side hit the Killie bar but the home side survived and held out for the three minutes of added time.
Celtic skipper Scott Brown, who had suffered a couple of hard challenges in the first half, was replaced at the interval by Mexican Efrain Juarez.
But there was no reasons to suspect the one-way traffic would not continue towards the Killie goal and four minutes after the restart Stokes had an attempt from 25 yards which Bell saved with a degree of comfort.
Still, it suggested a more direct attitude from the visitors and it paid off in the 51st minute when Stokes scored his first goal since signing from Hibernian just before transfer window closed.
Hoops’ Honduran left-back Emilio Izaguirre took a pass from Shaun Maloney and his cross from the left sped across the box leaving the Irishman to volley in from close range before taking the acclaim of the travelling fans behind the goal.
Kilmarnock brought on Danny Invincibile and new Portuguese signing Rui Miguel for Harry Forrester and Garry Hay respectively, as they tried to turn the tide.
The home side did push forward more and in the 77th minute Hoops’ stopper Daniel Majstorovic, who had taken the armband from Brown, put in a great tackle to prevent Sammon getting past him inside the Celtic penalty area.
But it was still mostly Celtic in the closing stages. Bell made a good save from a Maloney free-kick and then Izaguirre sent in a terrific cross from the left again which just evaded Juarez almost on the goalline.