The response of a Silicon Photomultiplier (SiPM) to optical signals is affected by many factors including photon-detection efficiency, recovery time, gain, optical crosstalk, afterpulsing, dark count, and detector dead time. Many of these parameters vary with overvoltage and temperature. When used to detect scintillation light, there is a complicated non-linear relationship between the incident light and the response of the SiPM. In this paper, we propose a combined discrete-time discrete-event Monte Carlo (MC) model to simulate SiPM response to scintillation light pulses. Our MC model accounts for all relevant aspects of the SiPM response, some of which were not accounted for in the previous models. We also derive and validate analytic expressions for the single-photoelectron response of the SiPM and the voltage drop across the quenching resistance in the SiPM microcell. These analytic expressions consider the effect of all the circuit elements in the SiPM and accurately simulate the time-variation in overvoltage across the microcells of the SiPM. Consequently, our MC model is able to incorporate the variation of the different SiPM parameters with varying overvoltage. The MC model is compared with measurements on SiPM-based scintillation detectors and with some cases for which the response is known a priori. The model is also used to study the variation in SiPM behavior with SiPM-circuit parameter variations and to predict the response of a SiPM-based detector to various scintillators.