Understanding quantum system dynamics driven by nonclassical light pulses is challenging, particularly for general light states with large photon numbers. Here we introduce an efficient framework that makes this task tractable. By introducing a pulse-shaped P-representation, the exact quantum evolution is decomposed into a mixture of many independent quasi-classical branches, each governed by a standard master equation with a classical pulse which can be solved efficiently. As an illustration, for a two-level system interacting with an exponential pulse, we first find out the exact analytical solutions to the Bloch equations in each quasi-classical branch, and then by taking proper P-function average over all branches, the full system dynamics driven by nonclassical light pulses is analytically obtained. For the one-/two-photon case, this approach well reproduces the previous results analytically/numerically, and also scales efficiently to more complex light states (Fock, thermal, squeezed vacuum photon statistics) with large photon numbers. Especially, for the Fock pulse with a Lorentzian profile, the analytical results for arbitrary photon numbers are obtained. We further provide a clear physical interpretation how the system dynamics is influenced through the high-order optical coherence of the nonclassical pulses. This work provides a unified and computationally efficient route and a useful starting point to explore more complex quantum dynamics driven by nonclassical light in quantum optics and quantum information processing.