Barcelona led through a Gerard Pique header but Madrid hit back with a spectacular Karim Benzema equaliser before Cristiano Ronaldo produced a brilliant winner.
Sergio Ramos was sent off for Madrid shortly before Ronaldo's goal, but Madrid were deserved winners having had a header by Gareth Bale controversially disallowed.
Madrid's win ended a run of 23 La Liga matches without defeat for Barcelona and leaves Zidane's side just seven points behind their rivals in the title race.
"[I am] Very proud of what the players did, this is not an easy ground, I'm very happy with everything, not just the result," Zidane told reporters after the match.
"These are [just] three points. Now we must think about resting well and the next game in the Champions League."
Real Madrid face Wolfsburg in the first leg of their Champions League quarter-final on Wednesday, but Zidane was happy to revel in his side's Clasico win for the time being.
"When I see us like that, united, giving everything for your team-mates, for a coach that is the best," he said.
"I liked everything about my team - in attack and defence. We made a huge effort against very good players.
"Our start was not so good, but better to start difficult and end well as we have done. Defensively we played an enormous game against very good players. With small space they can do you damage. And we controlled that well.
"We are on our path, preparing for the end of the season. We know we can do important things in the Champions League. "This can be a turning point. It is very important, for the rest of season, for our spirit. We must go step by step. First we must pass Atletico, we are still third. Then we'll see what happens.
"There are still games to play."
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