We discover hidden Rashba fine structure in CH$_3$NH$_3$PbI$_3$ and demonstrate its quantum control by vibrational coherence through symmetry-selective vibronic (electron-phonon) coupling. Above a critical threshold of a single-cycle terahertz pump field, a Raman phonon mode distinctly modulates the middle excitonic states with {em persistent} coherence for more than ten times longer than the ones on two sides that predominately couple to infrared phonons. These vibronic quantum beats, together with first-principles modeling of phonon periodically modulated Rashba parameters, identify a {em three-fold} excitonic fine structure splitting, i.e., optically-forbidden, degenerate dark states in between two bright ones. Harnessing of vibronic quantum coherence and symmetry inspires light-perovskite quantum control and sub-THz-cycle Rashba engineering of spin-split bands for ultimate multi-function device.
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