Real, who have dropped to sixth in the Spanish league, seven points off leaders Barcelona after six matches, were in sparkling European form, outclassing the Germans who had conceded just one goal in their first six Bundesliga matches.
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The result was even more significant for Real, who finally managed to get a first win at Dortmund after three defeats and three draws.
Cristiano Ronaldo, who last week started his first league game of the season following suspension, scored twice and Gareth Bale added another as they punished the Germans for giving them too much space.
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"We played a great game from start to finish. We could have scored more. We had chances," said Zidane. "We had a spectacular game, a brilliant game. The important thing is to score more than our opponents and we did that. I am delighted for Ronaldo and Bale. The side worked hard. The midfield worked very hard. I am extremely happy because they played a tremendous game."
The Frenchman praised his players for a focused and disciplined performance and for not losing their cool when Dortmund pulled a goal back early in the second half to make it 2-1 and set up a nerve-wracking final 25 minutes.
"We started well, the first half was brilliant as was the second,” he said. “We showed authority. We had some difficult moments after the break but we played them out. It was perfect.”
Real are on six points from two games in Group H, along with Tottenham Hotspur, who beat APOEL Nicosia 3-0 in Cyprus.
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