The jets of blazars are renowned for their multiwavelength flares and rapid extreme variability; however, there are still some important unanswered questions about the physical processes responsible for these spectral and temporal changes in emission properties. In this article, we develop a time-dependent particle evolution model for the time-varying emission spectrum of blazars. In the model, we introduce time-dependent electric and magnetic fields, which consistently include the variability of relevant physical quantities in the transport equation. The evolution of the electron distribution is solved numerically from a generalized transport equation that contains terms describing the electrostatic, first- and second-order Fermi acceleration, escape of particles due to both advection and spatial diffusion, and also energy losses due to synchrotron emission and inverse-Compton scattering of both synchrotron and external ambient photon fields. We find that the light-curve profiles of blazars are consistent with the particle spectral evolution resulting from time-dependent electric and magnetic fields, rather than the effects of acceleration or cooling processes. The proposed model is able to account simultaneously for the variability of both the energy spectrum and the light-curve profile of the BL Lac object Mrk 421, with reasonable assumptions about the physical parameters. The results indicate strongly that the magnetic field evolution in the dissipated region of a blazar jet can account for the variabilities.