Los Blancos fell behind to Joshua Kimmich's 28th-minute strike and struggled defensively in Wednesday night's semi-final first leg at the Allianz Arena.
However, Marcelo smashed home a half-volley from the edge of the penalty area on the stroke of half time before Marco Asensio capitalised on an error by Rafinha to score a breakaway goal just before the hour.
Real hung on for a 2-1 win in Bavaria which puts them in pole position to reach the final of the competition, and Zidane was a relieved man at full time.
"We played well, this is football," the Frenchman told Premium Sport. "They have had a lot of chances but we won, it was not easy at the beginning, then in the second half we improved.
"We suffered a lot, especially in the beginning. We have struggled and still managed to win. This team has the quality to overcome any obstacle. Isco, unfortunately, had to leave because of an injury."
The return leg takes place in six days' time at the Bernabeu, with the winner of the tie going on to face Liverpool or Roma in the final.