For a while it was patient rather than great football, and for a chunk of the afternoon Kilmarnock proved their equal in all departments, but the formidable sense of purpose that Martin O'Neill has engendered in Celtic since his arrival six months ago, allied to the sheer quality in their ranks, eventually gave the Glasgow team a comfortable victory yesterday, their 20th in the Scottish Premier League this season.
It meant that as Rangers prepared to meet St Mirren last night, Dick Advocaat's players knew that they needed a win just to keep the gap with their greatest rivals at 12 points. Celtic's lead over Hibernian is nine points. The transformation which O'Neill has wrought has been dramatic.
Ultimately this was an emphatic home win against a Kilmarnock side that began the day in fourth place and who, for an hour, justified a reputation for organisation and determination. But once Chris Sutton drilled in his second and Celtic's third in the 62nd minute the stuffing fell out of Bobby Williamson's team. Within another seven minutes Henrik Larsson had made it 4-0 and four minutes on from that Larsson clipped in the fifth. Kilmarnock were ragged.
It was the brilliant Swede's hat-trick goal. As if that was not sweet enough it was also his 100th for the club, in 138 appearances. Three minutes from the end Larsson then got a fourth, his 32nd of the season. And yet, somehow, Sutton was voted man of the match.
Still, Larsson will not care about personal awards. For all their individual skills the overriding characteristic of any O'Neill team is that it is just that - a team.
Yesterday it needed to be. The scoreline makes it sound straightforward, but anyone who had watched the opening 37 minutes would have been just as impressed with Kilmarnock as Celtic. Tight in the tackle, sprightly on the counterattack and in control at the back, the Ayrshire club were unruffled. Goalkeeper Gordon Marshall, back at his old ground, must have felt like the home 'keeper again. He did not have one save to make.
Small in physique, but big in attitude, Kilmarnock were frustrating Celtic to the extent that shortly before the breakthrough the loudest noise from another massive crowd was grumbling. Bobby Petta bore the brunt of the complaints, the winger consistently losing possession to a Kilmarnock defence in which the diminutive Gary Hay was outstanding.
It was ironic then that when Neil Lennon swept in a 30-yard diagonal cross in the 38th minute it found Hay just standing. Instead of attacking the ball as he had been doing, Hay watched it sail over his head. Taking the chance that that might happen, Sutton continued his run into the area and made a telling sliding connection. Marshall's first significant contribution was to pick the ball out of the net.
Three minutes before half-time Ramon Vega should have made it 2-0 but missed with a six-yard header, but there was little suggestion of the rout to come even when Larsson got his first of the game nine minutes after the interval.
The goal once again illustrated Larsson's intuitive knack for goalscoring. With the whole of Parkhead roaring for a penalty kick after Stilian Petrov had been upended by Gary Holt, Larsson ignored the appeals and played on. So did referee David Sommers. Larsson spiked the ball beyond Marshall.
Eight minutes later Sutton seized on Johan Mjallby's centre to make it three and after that Celtic began to play with attractive freedom and authority. As Kilmarnock dissolved, Lennon came to the fore, Didier Agathe roamed widely and Sutton and Larsson waited to pounce.
Larsson did so three more times. First from a cross from Petrov - 4-0. Then substitute Alan Thompson jinked his way through a couple of poor attempts at challenges - 5-0. And finally another substitute, Lubo Moravcik, supplied the last with three minutes remaining - 6-0.
At the end the atmosphere in the stadium was like a carnival, and the crowd even had a pantomime villain to jeer.
Ten minutes from the end Ally McCoist came on for the visitors. But by then this was not a question of sport. It was a New Year hunt. And Kilmarnock sounded more like an instruction rather than the name of a club.
Celtic: Douglas, Valgaeren, Mjallby, Vega, Agathe, McNamara (Smith 74), Lennon, Petrov (Moravcik 74), Petta (Thompson 69), Larsson, Sutton. Subs Not Used: Gould, Boyd. Booked: Valgaeren, Petta, Lennon. Goals: Sutton 37, Larsson 53, Sutton 61, Larsson 69, 72, 86.
Kilmarnock: Marshall, Hay, McGowne, Dindeleux (Innes 79), Canero, Cocard, Holt, Mahood, McLaren, Wright (Reilly 79), Dargo (McCoist 79). Subs Not Used: Meldrum, Canning. Booked: Canero, Wright.
Referee: D Somers (Scotland).