Fábregas, Messi, Fábregas, Messi. In the midst of a debate over the 'Barcelona Way', two men who played together for the club as 13-year-olds cut their way through Milan's defence and completed a victory that qualifies them for the knockout stages. But this was not just about winning, it was about convincing too. Vencer and convencer as the Spanish phrase has it.

When the two men twice exchanged passes and Lionel Messi lifted the ball expertly over Christian Abbiati seven minutes from time, Barcelona were already leading 2-1 and Messi had already ended his rather short "long" wait for a goal. But they had scored from a penalty and a set play, and since the introduction of Mario Balotelli, had not always been as comfortable as the first-half had suggested. Now they scored the way they were supposed to: slick and precise, Messi's feet flashing. This was more like it.

The pressure had been on Barcelona and Messi. Not so much for their results, which have been close to perfect, as their performances, a fierce and often exaggerated debate raged about their style. Tata Martino, the Barcelona manager, had joked that the team were in "crisis". His words carried a bitter sting. Messi had endured his longest run without a goal in two-and-half years. Four whole games. "Relax," his father Jorge had said, "he'll be back." Here, he was.

The drought ended within half an hour and from the penalty spot. As Neymar dashed into the area trying to reach Andrés Iniesta's clipped pass, he spun and tumbled to the ground under challenge from Ignazio Abate. The fall appeared exaggerated but there was little complaint from the Italians, just acceptance. Messi took the penalty in a manner that suggested vindication. Hard and straight, the thud off foot-on-ball could be heard high in the main stand. Barcelona were in the lead and in control, comfortable if not always incisive.

This was the third game in a row in which Messi had scored against Milan. And if Barcelona's crisis seemed to ebb away, Milan's is for real. They sit 11th in Serie A, 19 points behind the leaders, Roma, after only 11 games, and with a negative goal difference. Balotelli, left on the bench here, has more yellow cards than goals. Massimiliano Allegri, the manager, is on the ropes and Silvio Berlusconi's daughter Barbara has been forced to deny reports that she demanded the sacking of club administrator Adriano Galliani, who has been at the club for a quarter of a century.

There was something a little sad about watching them here; seven times European Cup winners, they waited for Barcelona, unable or unwilling to do any more. At one point they tried to take a short goal kick to draw Barcelona out; they almost let Barcelona in – Abbiati's clipped pass from next to his post rebounding off Alexis Sánchez's head and into the side netting. Set plays are rarely Barcelona's greatest weapon but Milan put up no resistance when Xavi's in-swinging free-kick was nodded in, entirely unopposed, by Sergio Busquets. He was barely eight yards out. But then Kaká turned and escaped Dani Alves on the left. He accelerated away, too fast for the full-back, and into the area. His pull-back deflected off Gerard Piqué and into the net. It was the final touch of the first half.

At the break, Balotelli was introduced in place of Robinho and soon he was wriggling free to fire off a shot that Victor Valdes saved. Maybe this game would not be so comfortable after all.

Barcelona had more of the ball still and occasionally looked like finding space behind Milan, with Abbiati turning one Iniesta shot around the post. But at the other end the threat was real now. Swift, sliding interceptions from Piqué and Javier Mascherano stopped Kaká and Sulley Muntari. On the right, Balotelli received, threw off Adriano and skipped past Mascherano. His pull-back was put just wide by Kaká.

Nervousness crept back in. There was applause when Neymar came dashing in from the left, and past four men, running horizontally across the area as opponents slipped to the floor. But the brilliance of the run was not matched by the shot, which was scuffed wide from 12 yards. He then combined with Messi to provide a chance for Alexis, superbly saved by Abbiati. Barcelona had reawakened. And when Fábregas was introduced soon after the impact was almost immediate.