Gordon Strachan strengthened his case to be named Scotland's manager of the year after leading champions Celtic to a comfortable victory at Rugby Park.
The result means Kilmarnock, who notched a late consolation through Colin Nish, remain a point behind fourth-placed Hibernian.
The Hoops boss made three changes, with Bobo Balde, Artur Boruc and Maciej Zurawski being rested to let in Stanislav Varga, making his fifth SPL appearance, David Marshall and Aiden McGeady.
Celtic partied hard after beating Hearts at Parkhead in midweek but nobody could accuse them of not caring about the rest of the season.
Nakamura curled them in front after just seven minutes after winning a free-kick himself, 22 yards from goal.
The Japanese playmaker was brought down by Steven Naismith and he ruthlessly punished the youngster by sending a left-footed shot over the wall and into the top corner, beyond Alan Combe's left hand.
Marshall had very little to do early on, apart from watch Gary Wales' shot sail high over the bar from the edge of the box.
The young goalkeeper also comfortably saved Colin Nish's weak strike from 15 yards, but perhaps Stephen McManus did enough to distract him.
It was an end-of-season stroll for Celtic until the final minute of the half when the game become embroiled in controversy.
Naismith had the ball in the net after quick-thinking from Wales, but linesman Frank Cole thrust his flag in the air to signal offside — even though the youngster looked to have been at least two yards on.
The officials were jeered as they left the field, but the referee went some way to evening things up by showing Petrov the first yellow card of the afternoon for a full-blooded challenge on Wright.
Scotland Under-21 international Naismith was a real handful and he almost brought the scores level on the hour mark.
Naismith seized on Hay's long ball but dinked the ball past Marshall and his far post from the edge of the box. The youngster again put the ball past the same post from Lennon's misplaced pass, to let the visitors off the hook again.
But that sparked the best possible response from Celtic, who doubled their advantage moments later.
Nakamura fed Maloney and despite Combe getting a hand to his cross, Hartson arrived at the back post to bundle the ball home for his 19th goal of the campaign.
Kilmarnock came roaring back and Marshall had to produce a brilliant save to stop Wales converting Naismith's pass. Invincibile then fired just over the angle before Stephen Pearson came on for Petrov.
Strachan introduced Dion Dublin for Hartson as the veteran former England man moved to within three games of guaranteeing a championship medal.
There was still time for Nakamura and Dublin to fire past Combe to move Celtic onto 85 points with five games left.
Nish provided Kilmarnock with a consolation in the dying seconds but Kilmarnock stay behind Hibernian in the battle for Europe.
