Even in their faded grandeur, AC Milan were still capable of reclaiming some of the old mastery.

The tensions of their recent collapse in esteem have undermined much of the team's accomplishment, but flashes of aplomb were still possible. They ought to have been reduced to their neuroses at Celtic Park, having not won an away game all season and been riven by power struggles, rivalries and a steep decline in quality. Yet, in the midst of what began as an intense atmosphere, the hostilities were banished.

Kaka does not possess the energy and surging brilliance of his youth, but he could still on occasion gallop with elegance and grace through a packed midfield. His worth to the visitors was not in that rangy, languid style, though, so much as his expertise, the instincts of a player who was once imperious and coveted as one of the greats of his generation.

The Brazilian offered experience in the final third, so that when Milan cleared the ball upfield, it often remained there, allowing the visitors to establish an air of authority. More significantly, Kaka was in the right place at the right time to take advantage of irresponsible Celtic defending. His header from close range was a scuffed effort compared to past stylish goals, but it removed any self-doubt the visitors might have brought with them from Italy.

Milan's domestic form has brought a lowly distinction. They are without a win in five matches, their worst run in six years, and they are in the bottom half of Serie A. Only the tussle for control between Adriano Galliani, the long-time chief executive, and Barbara Berlusconi, the daughter of the club's owner, have prevented intolerable pressure being applied to the coach, Massimilliano Allegri.

In truth, though, Allegri has switched between different tactics and personnel in a bid to wrest a level of form and consistency from a group of players who are pale shadows of past glories. The Milan fans made their discontent known at the weekend, when around 300 waited outside San Siro following a 1-1 draw with Genoa, and were addressed by Kaka and Christian Abbiati, two of the most senior and popular members of the squad.

Yet stories still emerge of Mario Balotelli turning up late for training. The striker tends to be indulged, because of the brilliant unpredictability of his talent. He often ambles around with casual indifference, but he is transformed when the ball is within his vicinity. Neither Celtic centre-back could relax, however sullen Balotelli looked. It was a rebuke to the hosts' defending that when the Italian struck the game's third goal, it was from a long ball up the middle of the pitch and the only rarefied touch was the one Balotelli used to bring it under control before stabbing a shot beyond Fraser Forster.

The Milan players celebrated with each other and the bench. Pundits in Italy talk about who might best replace the coach, with candidates from either side of the power divide inside the club: Galliani's favourites and Berlusconi's favourites. It is a dysfunctional environment, but Milan are European aristocracy, their history is of a club that asserts its worth in the premier competition, and the Champions League still provides a dose of self-belief.

This was still a diminished version of Milan, though. Every area of the team could not compare to past incarnations. Even Balotelli, who is the undoubted star - at least in terms of his quality - is a reduction. Zvonimir Boban, the former AC Milan midfielder, remarked that Paolo Maldini or Franco Baresi would have slapped Balotelli for turning up late. In last night's match programme, an extract from Andrea Pirlo's autobiography detailed how the Milan players would often seek advice in all aspects of their lives from Maldini or Billy Costacurta.

That hierarchy is no longer in place, and in the same way that Italian football has struggled to keep pace with the riches and acumen of the other major leagues in Europe, so too have Milan lost the financial might to compete in the transfer market. Compromises have been made, leaving the team short of the wherewithal to meet its obligations. They were often anxious in defence last night, not least when Abbiati was punching clear rather than catching it, but there was little pressure applied and the visitors were able to control of the game.

Chances came with relative ease, at least at set pieces, and Cristian Zapata could not fail to score the just after half time when the ball fell to him only a yard from goal. This was a restorative night for Milan, one in which the current crisis could be briefly forgotten.