The Los Blancos manager took off Toni Kroos and Isco for Lucas Vazquez and Vinicius Junior at the break after Atleti outplayed his side:
The switch worked. Vinicius played a key role in Karim Benzema's 56th-minute goal, which secured Real a rare home victory against their city rivals in the league:
Zidane told reporters after the win that the changes were necessary because he set up the team wrong: "I had to change things. I wasn't happy with what I was seeing, but it wasn't the players' fault; it was mine. I didn't want to point a finger at anyone, even less so at Isco and Toni, who are very good players. I'm happy for the win, for all of the players, and everyone is happy with the result."
Having started with five midfielders, Real switched to a 4-3-3 formation in the second half.
Benzema turned home from six yards after Vinicius fed Ferland Mendy in space in the left channel and the left-back squared across the box.
It was the Frenchman's 13th league goal of the season. Only Lionel Messi has netted more with 14.
Real have won four on the bounce in La Liga and have not lost a game in the Spanish top flight since October's 1-0 reverse at Mallorca in an unbeaten run of 13 games.
They are the clear front-runners for the La Liga title given Barca have been showing variable form under new manager Quique Setien. Real moved six points clear at the top ahead of Barcelona's clash against Levante on Sunday.
Even though the squad is largely the same, Real look a different prospect from last season, when their title challenge never materialised and both Julen Lopetegui and Santiago Solari were sacked in the course of the campaign.
Much of the credit should be given to Zidane:
His record as Real manager is staggering. In his first two-and-a-half-year spell in charge, he won nine trophies, including three successive UEFA Champions Leagues.
Since his return to the Santiago Bernabeu dugout last March, Zidane has added the Spanish Super Cup for his 10th, and it would be a surprise were more not forthcoming in the remainder of the season.