The question here has two parts: 1) According to Judaism, does black magic exist? 2) How does this fit into the Jewish belief that nothing happens against the will of G-d?
The Talmud (Sanhedrin 67b) makes a statement that clearly addresses these issues in a cryptic way:
אמר רבי יוחנן למה נקרא שמן כשפים שמכחישין פמליא של מעלה:
(דברים ד, לה) אין עוד מלבדו אמר רבי חנינא אפילו לדבר כשפים
Rabbi Yoḥanan says: Why is sorcery called keshafim? Because it is an acronym for: Contradicts the heavenly entourage [shemakhḥishin pamalia shel mala]. Sorcery appears to contradict the laws of nature established by God.
The verse states: “To you it was shown, so that you should know that the Lord is God; there is none else besides Him” (Deuteronomy 4:35). Rabbi Ḥanina says: This is true even with regard to a matter of sorcery.
The Ramchal (Daas Tevunos siman 36) explains:
שאף על פי שלפי סדרי המערכה העליונה שרצה הקב"ה וערך, הנה כשפים מכחישים פמליא של מעלה (סנהדרין שם), הנה כשהוא רוצה - מושל בכוחו ומבטלם, והיו כלא היו, ולא כשחשבו הפתאים שיוכלו להשתמש מכליו עצמם כנגדו ח"ו:
That even though according to the order of the array of the heavens that the Holy One blessed is He wanted and arranged, sorcery contradicts the family of the heavens (Sanhedrin 67b), behold when he wants - he rules with his power and nullifies them, and they are as if they never existed, and not as the naive thought, that they could use His utensils themselves against Him, G-d forbid.