Hydrogen bonding plays a foundational role in the life, earth, and chemical sciences, with its richness and strength depending on the situation. In molecular materials, these interactions determine assembly mechanisms, control superconductivity, and even permit magnetic exchange. In spite of its long-standing importance, exquisite control of hydrogen bonding in molecule-based magnets has only been realized in limited form and remains as one of the major challenges. Here, we report the discovery that pressure can tune the dimensionality of hydrogen bonding networks in CuF₂(H₂O)₂(3-chloropyridine) to induce magnetic switching. Specifically, we reveal how the development of O-H···Cl exchange pathways under compression combined with an enhanced ab-plane hydrogen bonding network yields a three dimensional superexchange web between copper centers that triggers a reversible magnetic crossover. Similar pressure- and strain-driven crossover mechanisms involving coordinated motion of hydrogen bond networks may play out in other quantum magnets.