Magnetic single atoms and molecules are receiving intensifying research focus because of their potential as the smallest possible memory, spintronic, and qubit elements. Scanning probe microscopes used to study these systems have benefited greatly from new techniques that use molecule-functionalized tips to enhance spatial and spectroscopic resolutions and enable new sensing capabilities. We demonstrate a microscopy technique that uses a magnetic molecule, Ni(cyclopentadienyl)(2), adsorbed at the apex of a scanning probe tip, to sense exchange interactions with another molecule adsorbed on a Ag(110) surface in a continuously tunable fashion in all three spatial directions. We further used the probe to image contours of exchange interaction strength, revealing angstrom-scale regions where the quantum states of two magnetic molecules strongly mix. Our results pave the way for new nanoscale imaging capabilities based on magnetic single-molecule sensors.