Out-of-contract Stanislav Varga gave Gordon Strachan a further nudge as the runaway Bank of Scotland Premier League champions killed off Kilmarnock's outside hopes of a UEFA Cup place.

The Slovakian has come in from the cold in recent weeks with Bobo Balde injured - and his case for a new contract has not been helped by his team-mates taking things easy with the title easily wrapped up.

But Varga will arrive at the manager's office with a feather in his cap after capping a better second-half Celtic performance.

Maciej Zurawski set up the success, after the defeat at Hearts, with his 20th goal of the season after a lifeless first-half.

Double-winning Strachan gave his fringe men a chance to stake their places with six changes from Tynecastle but in an uneventful first-half they did little to prove they could cut it.

David Marshall, Ross Wallace, Stilian Petrov, Aiden McGeady, Alan Thompson and Stephen Pearson came in for Artur Boruc, Paul Telfer, Shaun Maloney, Dion Dublin, Neil Lennon and Shunsuke Nakamura.

Kilmarnock manager Jim Jefferies made just one change with Peter Leven coming in for Garry Hay.

Celtic had been going through the motions since winning the title weeks ago and Killie gave them a scare after just two minutes.

Leven's long throw was allowed to bounce and football writers' young player of the year Steven Naismith got in ahead of Varga to put the ball over from close range.

David Marshall gave the low home side a fright of a different kind moments later when he came off worse in a crunching slide challenge with Colin Nish - but he recovered after some attention.

Forgotten man Thompson rolled back the years in the 10th minute with a delicate chip to send Petrov clean through - but the want-away midfielder's right-foot was drive saved by Alan Combe.

The Bulgarian would have been through again, from McGeady's pass, in the 14th minute but for Frazer Wright's important intervention.

Wright was again in the right place at the right time in the 37th minute as Zurawski tried to pick out Pearson at the back post.

But Gary Wales should have headed the visitors into the lead five minutes before half-time when Danny Invincibile picked him out, seven yards from goal, but he put his effort straight at Marshall.

Zurawski brought the crowd to life in the third minute of the second half having been picked out by Roy Keane.

The Polish star did brilliantly to take the ball in his stride but Combe was alert to rush off his line to save at his feet.

The crowd expected something special in the 55th minute when the ball fell to Keane after Pearson had left James Fowler and Leven for dead - but the Irishman sliced his shot horribly wide from 20 yards.

But Celtic went ahead moments later as Zurawski converted their best move of the night.

Keane played the ball out wide to Mark Wilson and he picked out the Pole, who slotted the ball home at the far post.

Varga then strengthened his case for a new contract in the 64th minute by heading Wallace's inviting cross past Combe from six yards.

Moments later and players' young player and player of the year Maloney came on for McGeady.

Jefferies knew any hopes of fourth place had evaporated and he brought on Paul di Giacomo for Wales seconds later.

Nish could have reduced the deficit late on but he drove over the top from eight yards.

Dublin could have capped his arrival from the bench with the third but he watched his shot, from Wilson's cross, well saved by Combe.

At the final whistle the Celtic players were saluted by their fans, who also celebrated Rangers' Champions League upset.

Teams

Celtic Marshall, Wilson, Varga, McManus, Wallace (Virgo 86),McGeady (Maloney 64), Keane, Petrov, Thompson, Zurawski (Dublin 83), Pearson.

Subs Not Used: Boruc, Telfer, Lennon, Camara.

Goals: Zurawski 55, Varga 63.

Kilmarnock Combe, Fowler, Greer, Wright, Wilson (Locke 67),Leven, Wales (Di Giacomo 64), Johnston, Invincibile, Nish,Naismith.

Subs Not Used: Smith, McDonald, Murray, Campbell, Bell.

Att: 48,649

Ref: S Conroy (Scotland).