The Danish midfielder’s first-half double seemed to have the visitors cruising but the champions panicked for a spell when Paisley striker John Sutton pulled a goal back eleven minutes after the break.

However, when the former Real Madrid player headed home a Shunsuke Nakamura corner, despite the best efforts of Saints midfielder Garry Brady to clear, the points were destined for Parkhead.

There was no real surprise that Gordon Strachan’s side took the points.

Those looking for omens in this game would have been guided towards a win for the visitors, as the Saints had not scored in their previous nine meetings with Celtic – a dubious record stretching all the way back to the 1991/92 season when they drew 1-1.

And it took only two minutes for the champions to take the lead.

A searching Lee Naylor cross from the left was met at the back post by Hoops’ striker Jan Vennegoor of Hesselink, who headed towards Kenny Miller as he headed towards the centre of the six-yard box.

The ball broke from the Scotland striker back to Gravesen who wasted no time in driving a left-footed shot from 14 yards past Saints keeper Tony Bullock.

And in the 20th minute, when Gravesen made it 2-0, the match seemed over.

The Dane took a Gary Caldwell pass 25 yards from goal, and, after looking to make some space for a pass without being closed down, he decided to take a shot and his effort swerved low past the stranded Bullock.

Another Hoops attack ended when Jan Vennegoor of Hesselink scooped an angled-drive from 12 yards over the bar after a clever Nakamura pass had put him through.

Miller was denied what looked like a good penalty claim when he was brought down in the St Mirren box by Kirk Broadfoot, but referee Stuart Dougal surprisingly pointed to a goal kick, the already two-goal lead probably dampening down any great protests from the visitors.

Few would have bet on a comeback by the home side at the interval and although the half-time pep talk had obviously invigorated the St Mirren players, it was Miller’s weak left-footed effort which trundled through to Bullock that opened up the second period.

The champions were in complete control but in the 52nd minute a dreadful moment of carelessness by Hoops keeper Artur Boruc almost handed the Saints a lifeline.

With no danger imminent, the Polish keeper clattered his attempted clearance straight at Sutton, but he made up for his mistake by saving the striker’s effort from 12 yards out before again blocking Billy Mehmet’s drive from the rebound.

Moments later there was another let-off for the Parkhead men when Mehmet crashed a header from a Simon Lappin cross off the post, but the Celtic defence, now panicking, could only hold on for another few seconds.

In the 56th minute Lappin’s pin-point cross from the left was met by Sutton six-yards from goal and the former Dundee player bulleted his header past Boruc.

However, in the 70th minute the visitors restored their two-goal advantage when Gravesen scored again to record his first hat-trick in a Celtic jersey.

A Nakamura corner from the right was met by the head of the Dane 12 yards out and although Brady tried to clear at the far post, referee Dougal took the advice of his assistant referee and signalled the goal.

Then, Celtic substitute Maciej Zurawski, who had replaced Miller, missed a good chance to make it four when, with only Bullock to beat, he dragged his angled shot wide of the far post.

But by that time most of the fight had gone out of the home side and the points were secured for the visitors, who continue their procession towards the title.