Reflectionless states (RLs) and exceptional points (EPs) are hallmark singular responses of non-Hermitian systems, with potential applications in sensing, wave control, and energy manipulation. Yet, realizing and independently tuning these states in a compact integrated platform remains challenging. Here, we demonstrate two-dimensional magnetic control of RLs and EPs in an on-chip magnon-phonon system based on a FeGaB-32 degree-YX-LiNbO3 heterostructure. The magnetic-field magnitude tunes the magnon-phonon detuning, driving a low-loss reflection zero across the real-frequency axis and producing two field-tunable RLs with near-vanishing reflection. A closed contour of the experimentally measured complex S11 around the reflection-zero singularity accumulates a -2pi phase winding. Independently, rotating the magnetic field tunes the magnon-phonon coupling strength, driving the intrinsic magnon-phonon eigenmode spectrum across an exceptional point, identified by the exchange between real-part and imaginary-part eigenvalue splitting. A unified one-port input-output model connects the measured complex S11 response to the field-driven dynamics of the reflection zeros and the angle-tuned intrinsic magnon-phonon eigenmodes. These results establish a magnetically programmable non-Hermitian magnon-phonon platform for integrated wave control and compact vector magnetic sensing.