Two minutes, two gifts, two goals and it was over before it had really begun. José Mourinho became the first coach in Real Madrid's history to remain unbeaten in his first 10 games – and the record was never in doubt. So quickly did the game appear to be resolved, so swiftly the record secured, that the Portuguese could have been forgiven for turning his thoughts to the future and a previously impossible dream: Wayne Rooney.

Back in May, before he had even joined Real Madrid or won this competition with Internazionale, Mourinho was asked which player he would most like to work with. "I am going to tell you because it is impossible," he replied. "I would like to coach Rooney, both because of the way he is as a footballer and also because of his mentality." But he added: "My friend [Alex] Ferguson can rest easy because it is impossible."

Is? Was. The extraordinary events of this week have changed the panorama. Florentino Pérez is a long-term admirer too, insiders admitting during his last mandate – four years ago – that the Madrid president was "crazy for Rooney". Imagine him alongside Ronaldo, winners of this tournament together in 2008 and finalists in 2009.

Tonight Mourinho reiterated his desire to sign Rooney: "I believe he is going to stay. But if at the end of the day Man United decide that he is to leave, then give me a call ... Everybody will be interested. But I like him, I like Sir Alex, I like Man United and I believe the best thing for him is to stay there for life."

Madrid proved they are potent enough without the England striker and Mourinho was happy with his team's performance. "This was an important test," he said. "We were too quick for Milan. If it was easy that was down to us. I don't think it's a case of Milan playing badly but a case of us playing very well. Pepe and [Ricardo] Carvalho play with their eyes closed, they know each other very well. [Zlatan] Ibrahimovic will always be a top striker for me, even if he had a hard night tonight"

Not that there was too much wrong with Madrid without the England striker. And it was the ease of the opening exchanges which permitted a spot of forward thinking.

By lasting until the 18th minute, Madrid would have broken a record for never having trailed since the start of the season. In the end, they did not even have to wait that long. This match had not even reached the quarter-hour mark yet Madrid, steaming out of the blocks, with Ronaldo running at the ageing Gianluca Zambrotta on the left, were two up. A place in the next round – beyond which Madrid have not progressed in six years – is virtually secure with three games to spare.

Milan's Alexandre Pato fouled Xabi Alonso on the edge of the area. The free‑kick appeared too close for Ronaldo but Ibrahimovic and Clarence Seedorf obligingly provided an opening in the wall and the ball sailed straight through.

Milan had barely digested what had happened when, a minute later, Ronaldo again ran at Zambrotta. His pull‑back found Mesut Ozil, whose scuffed shot deflected off Daniele Bonera and beyond Marco Amelia. The goalkeeper, making his debut, had been included only at the last minute because of an injury to Christian Abiatti. Milan had never before been two down so early in the tournament. A shot from Andrea Pirlo came back off the bar but they did not look like turning it round either.

Alonso exercised control. Ronaldo's pace and direct running, sticking this time to the left rather than swapping wings, caused constant problems. And Angel Di María too, although he passed up a couple of opportunities, was finding space on the other side – with Marcelo bombing beyond him from deep. Moving smoothly behind them, combining with his team-mates, Ozil confirmed his impressive form of late. Gonzalo Higuaín's best opportunity, heading Di María's cross, was saved. He had been perhaps the least impressive of the forwards.

There were few worrying moments for a defence led by the Portuguese partnership of Pepe and Carvalho. Zlatan Ibrahimovic's impact was nil. Ronaldinho, almost as peripheral, was removed for Robinho – who was greeted with boos, whistles and chants of "Robinho, die".

For Mourinho there was satisfaction. If Madrid's previous nine matches had not counted, barely considered a serious test, this certainly was. At last, it was said, here was a proper examination. Madrid passed it with ease and time to spare.