By Colin Moffat
Jan Vennegoor of Hesselink opened the scoring at Rugby Park.
Celtic wrapped up the Premier League title with four games to play thanks to a stunning last-minute free kick from Shunsuke Nakamura.
Jan Vennegoor of Hesselink headed Celtic in front from a Nakamura corner kick after 24 minutes.
Peter Leven and Steven Naismith missed glaring chances for Killie before good work from Gary Wales set up Colin Nish for a simple tap-in after the break.
But Nakamura curled in a wonderful strike from 22 yards to seal the win.
Celtic manager Gordon Strachan has now emulated his predecessor Martin O'Neill by winning back-to-back titles in his first two years at the club.
Celtic defender John Kennedy returned for the first time in more than three years following the terrible knee injury sustained on his Scotland debut.
But he had little to do in the opening stages as the visitors began brightly, with both Paul Hartley and Derek Riordan going close with strikes from distance.
Killie hit back with a shot from Nish and a Wales header was knocked off the line by Riordan, although Artur Boruc looked perfectly placed to save.
Celtic went ahead when Vennegoor of Hesselink rose highest in a congested penalty box to glance in a corner from Nakamura.
Peter Leven squandered a great chance to level immediately when he sent a free header over the top from seven yards.
Celtic skipper Neil Lennon then threatened a rare goal but Killie keeper Alan Combe got fingertips to his fierce 25-yard shot.
High crosses continued to cause problems for both sides and Vennegoor of Hesselink flashed a header wide before Steven Pressley's powerful nod was kept out by Combe.
Right on half-time, home striker Steven Naismith was given a clear sight of goal a few yards out but tentatively poked at the ball, allowing Boruc to save. Celtic were claiming for a penalty early in the second half when a Thomas Gravesen shot was deflected off-course by the hand of Grant Murray.
Having enjoyed that let-off, Kilmarnock raced up the park and equalised.
Wales did well to skip past Darren O'Dea and get to the by-line and, with Boruc covering his near post, his inviting cut-back was tucked into an empty net by Nish.
Naismith then found room in the Celtic penalty area but Boruc got down well to block the striker's shot and Wales sent a curling effort narrowly wide from 18 yards.
Celtic replied with a drilled dig from Nakamura that Combe did well to hold and Riordan skewed a shot wide after a penalty box scramble.
With 89 minutes on the clock, the ball broke to Riordan on the angle of the six yard box but the Celtic forward blazed the ball high and wide.
However, Nakamura had the last say when he curled a sweet strike round the defensive wall and beyond the static Combe.
WOHOOOOOOOOOOOOOOOOOOCHAMPIONEES,CHAMPIONEES,OLA,OLA,OLA.................................
