Cristiano Ronaldo delivered the knockout blow for Real Madrid in their aristocratic battle with AC Milan on Tuesday, as Arsenal, Chelsea and Bayern Munich maintained their own perfect Champions League starts.

While Arsenal provided a breathtaking collective display in a 5-1 win over Shakhtar Donetsk, nine-times European champions Real had the individual brilliance of the world's most expensive player to thank for their 2-0 win at the Bernabeu.

Ronaldo poked a free-kick straight through the wall and set up Mesut Ozil to score a heavily deflected second less than a minute later as Real saw off the seven-times winners with a devastating one-two combination.

Real and Milan make the record of Bayern Munich, the four-times winners, look relatively modest and there was a lot less style about their 3-2 home win over CFR Cluj in Group E, which saw them come from behind to take the lead with two own-goals before Mario Gomez gave them breathing space.

The only question mark over Jose Mourinho's Real Madrid early in the season was a struggle to turn their dominance into goals but that problem is now well behind them.

The Spanish league leaders followed up a 4-1 win over Malaga at the weekend with another performance of energy and guile, capped by goals in the 13th and 14th minutes.

"We needed to impose a strong rhythm from the start, playing with the concentration this type of game deserves, and we were able to do that," Ronaldo told reporters.

The Champions League, held up as the flagship of European club soccer, once again looked embarrassingly easy for Arsenal as they hammered Ukrainian champions Shakhtar Donetsk 5-1.

Alex Song, Samir Nasri, Cesc Fabregas, Jack Wilshere and Marouane Chamakh picked off the goals in a 5-1 win, with former Arsenal player Eduardo da Silva getting a late consolation for the visitors and a heartwarming ovation for himself.

The Group H demolition followed on from a 3-1 win in Belgrade and the 6-0 rout of Portuguese side Braga last month and their form in Europe has been in stark contrast to the weekly traumas they endure on the home front.

With a competition record 14 goals from their first three group matches and Manchester United's mark of 20 in their sights, fans could be forgiven for wondering what all the fuss is about UEFA's blue riband competition.

Whatever the relative strengths of some of the so-called "champions" put before them so far this season, Arsenal manager Arsene Wenger was delighted by the quality of his vibrant side's attacking panache on Tuesday.

Five different scorers was proof of the goal threat that his side possess, and even Shakhtar's late consolation was scored by Eduardo, the popular Brazilian-born Croatian who left north London for eastern Europe in June.

"When you win 1-0 people say it's too difficult and when you win 5-1 people say it's too easy," Wenger told reporters after first half goals from Alex Song and Samir Nasri laid the foundations for a thrashing completed after the break by Cesc Fabregas, Jack Wilshere and Marouane Chamakh.

"It's difficult to assess why we won 5-1. I think tonight we were intelligent able played to a very good technical level.

"The teams we play in the Champions League are used to dominating the games in their (domestic) championship so they don't come here to defend. Then when you are superior you always have the chance to score goals.

"The points were important, not the number of goals," he added.

Chelsea made a triumphant return to the scene of their most painful Champions League defeat when they beat Spartak Moscow 2-0 in a top-of-the-table Group F match.

Russia left back Yuri Zhirkov put the London club, beaten by Manchester United in the 2008 final after a penalty shootout at the same Luzhniki Stadium, ahead before French striker Nicolas Anelka doubled the lead just before the break.

Zhirkov, familiar with the artificial pitch after spending five seasons with Spartak's bitter Moscow rivals CSKA, pounced on a loose ball in the 23rd minute and volleyed spectacularly into the top corner of the net from 20 metres.

Anelka, who wasted a good chance to make it 2-0 when he lost control of the ball with the goal at his mercy, made amends in the 43rd minute by racing through the defence before driving low past keeper Andriy Dykan.

It was Anelka's 50th goal for Chelsea and Zhirkov's first since his move to Stamford Bridge in July 2009 as the English champions recorded their 50th win in 98 games in Europe's premier club competition.

Beneath the perfect quartet, Ajax Amsterdam maintained their hopes in Real Madrid's group by winning 2-1 at home to Auxerre, a result that took them level with Milan on four points.

Goals from Brazilian strikers Lima and Matheus gave Braga their first points with a 2-0 win over Partizan Belgrade that leaves the Serbs bottom of Group H.

Basel sprang a surprise in Group E by winning 3-1 away to AS Roma after two defeats, while Olympique Marseille kept their Group F hopes alive as they laboured to a 1-0 home win against Slovakians Zilina.