Intense multiterahertz fields of order megavolts per centimeter are used to coherently promote optically dark and dense paraexcitons in Cu2O from the 1s into the 2p state. The nonlinear field response of the intraexcitonic degrees of freedom is directly monitored in the time domain via ultrabroadband electro-optic sampling. The experimental results are analyzed with a microscopic many-body theory, identifying up to two internal Rabi cycles. The effects of population inversion and ponderomotive contributions are disentangled.