Aritz Aduriz cancelled out a first-half Karim Benzema effort to leave the two teams level in the second period, but Casemiro's close-range effort in the 68th minute saw Los Blancos record a 2-1 win in the La Liga fixture.
Zidane, whose team have moved five points clear at the top of the table, has said that "it was important to pick up points" entering the international break.
"We won at a difficult place, we suffered a lot but at the same time with character," Zidane told reporters. "It was important to pick up points and continue our good run. We have 11 matches left and we're top, but this means nothing. We know that there are more difficult matches to come."
Real Madrid have now won 20 of their 27 La Liga fixtures this season.