The study of brain network interactions during naturalistic stimuli facilitates a deeper understanding of human brain function. To estimate large-scale brain networks evoked with naturalistic stimuli, a tensor component analysis (TCA) based framework was used to characterize shared spatio-temporal patterns across subjects in a purely data-driven manner. In this framework, a third-order tensor is constructed from the timeseries extracted from all brain regions from a given parcellation, for all participants, with modes of the tensor corresponding to spatial distribution, time series and participants. TCA then reveals spatially and temporally shared components, i.e., evoked networks with the naturalistic stimuli, their time courses of activity and subject loadings of each component. To enhance the reproducibility of the estimation with the adaptive TCA algorithm, a novel spectral clustering method, tensor spectral clustering, was proposed and applied to evaluate the stability of the TCA algorithm. We demonstrated the effectiveness of the proposed framework via simulations and real fMRI data collected during a motor task with a traditional fMRI study design. We also applied the proposed framework to fMRI data collected during passive movie watching to illustrate how reproducible brain networks are evoked by naturalistic movie viewing.