Youssef El-Arabi cancelled out Karim Benzema's first-half opener at Los Carmenes and Madrid looked set to fall further adrift of La Liga leaders Barcelona after another stuttering performance on the road.
Modric proved the hero for the capital club, however, blasting the winner into the top corner from 25 yards with just five minutes remaining.
And Zidane was delighted with what proved to be a telling contribution from his playmaker, who he encouraged to try his luck more often.
"He scored a golazo and gave us life," he told reporters after the match. "Above all, he gave us three points. I'm happy for him. He has to shoot more because he has a good strike."
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Zidane has seen his side win 5-1, 5-0 and 6-0 at home but his only away game before Sunday since replacing Rafael Benitez as head coach ended in a 1-1 draw with Real Betis.
The former midfielder says Madrid should not be expected to win by the same sort of scoreline on the road and praised the attitude of his players following the victory.
"You also have to think that there's a team opposite us and the crowd are against us. It's normal that it's more difficult away," he said.
"We leave with the three points. They're very important. It takes a lot out of us because they are difficult pitches. Granada have good players who put you in difficulty.
"I'm happy with the attitude of the players. We were not going to win easily. I'm very proud."
Madrid host Athletic Bilbao next week before their Champions League campaign resumes against Roma, and Zidane says they are fully prepared for the last 16.
"Madrid are ready for the Champions League. You always have difficulty in every game, but we're ready," he said.
There was some concern over Marcelo at full-time after the Brazilian fell awkwardly after challenging for an aerial ball, and Zidane revealed there will likely be further tests to determine the problem.
He added: "Dani Carvajal has nothing, it's a minor thing. We still don't know what Marcelo has."