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.
Celtic can now look forward to next week's Scottish Cup semi-final against Hearts at Hampden and on this form, Neil Lennon's side must be favourites for the double.
Lennon, who was given a hero's reception by the Celtic fans after the game, was certainly vindicated in the three changes he made for the trip to Ayrshire.
In came right-back Adam Matthews, stopper Kelvin Wilson and midfielder Ki Sung-yueng with Mikael Lustig, Thomas Rogne and Anthony Stokes dropping out, with only the Irishman starting on the bench.
Killie's on-loan defender Lewis Toshney was not allowed to play against his parent club and his place was taken by Liam Kelly.
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.
The move to accommodate the hordes of Hoops fans looking to attend what they hoped would be a title party made around £150,000 for Killie's coffers but it was akin to a home game for Lennon's men with a matching atmosphere which helped the visitors race into an early two-goal lead.
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 all too easily drifted in from the left before curling his shot past Bell and into the far corner.
Moments later only a brilliant block from the foot of Bell prevented Samaras making it four, after the Greece striker had been unselfishly set up by Commons 12 yards from goal.
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.
Killie boss Kenny Shiels replaced Garry Hay and Lee Johnson with James Dayton and Ross Barbour for the start of the second half while Filip Twardzik soon came on for Hoops skipper Brown.
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 Kelly firing high over the bar from outside the box.
Celtic fans rejoiced, mostly in the possible demise of their administration-hit Old Firm rivals Rangers.
In the 62nd minute, in a swift Celtic counter, Commons sent Loovens through on goal but the big Dutchman shot wide as he collided with Bell, both players continuing after treatment.
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.
The travelling fans in the crowd of 15,926 stepped up their celebrations all the way to the final whistle which brought a huge roar as the Hoops claimed the 43rd league title in their history.