We have investigated the mechanism of para-hydrogen-induced polarization (PHIP) transfer from the original strongly aligned protons to other nuclei at low external magnetic fields. Although it is known that PHIP is efficiently transferred at low fields, the nature of the transfer mechanism, that is, coherent spin mixing or cross-relaxation, is not well established. Polarization transfer kinetics for individual protons of styrene was, for the first time, measured and modeled theoretically. Pronounced oscillations were observed indicating a coherent transfer mechanism. Spin coherences were excited by passing through an avoided level crossing of the nuclear spin energy levels. Transfer at avoided level crossings is selective with respect to spin order. Our work provides evidence that the coherent PHIP transfer mechanism is dominant at low magnetic fields.