Left-back Charlie Mulgrew was the force behind their first half domination, scoring twice and setting up goals for Glenn Loovens and Gary Hooper to give the rampant visitors an unassailable interval lead.
In what was one of the most impressive performances of the season, late goals by midfielder Joe Ledley and Hooper confirmed with some conviction that the championship is back at Parkhead for the first time in four years.
Kilmarnock had beaten Celtic in the Scottish Communities League Cup final at Hampden last month but, with the mood the Parkhead men were in, there was never any chance of a repeat. The Ayrshire club had moved some of their supporters from the East Stand to allow Celtic fans three of the four stands at Rugby Park.
Celtic started strongly with Kris Commons pushed up alongside Georgios Samaras and Hooper but it was Mulgrew who headed them into the lead after only seven minutes. Ki's powerful drive was deflected for a corner and when the South Korean swung the ball in from the left, Mulgrew rose high inside the six yard box to steer the ball into the net.
From then on it was all Celtic and all Mulgrew. In the 16th minute he took a Scott Brown pass wide on the right before swinging in a cross to the back post where the unmarked Loovens headed past Cameron Bell for his first goal of the season.
Celtic were overwhelming a startled Killie side who did not have any sort of antidote and in the 34th minute Mulgrew drifted in from the left before curling his shot past Bell and into the far corner. It was too easy for the visitors and a minute from the break, from wide on the left, Mulgrew crossed to the back post for Hooper to volley high past the helpless Bell.
Celtic were free-wheeling while it was purely a damage limitation exercise for the bewildered home side although a brief spell of pressure on the Celtic goal in the 52nd minute ended with Liam Kelly firing high over the bar from outside the box.
Anthony Stokes, who had replaced Samaras, had a great chance in the 75th minute when he was sent clean through by Mulgrew but the former Sunderland player hesitated in possession and was robbed by back-tracking Killie defender Mo Sissoko.
Two minutes from time Ledley grabbed the fifth with a dink over Bell after the Killie defence crumbled before Hooper volleyed in number six a minute later to seal a commanding performance.
Source: PA
Source: PA