Upright faces are considered to be processed more holistically than inverted faces in the face inversion and face composite as well as parts-whole paradigms. However, little is known about whether the holistic face processing is affected by face orientation in the conflict tasks, which computations characterize cognitive control mechanisms of upright and inverted faces in these conflict tasks, and whether the holistic cognitive control mechanism is manifested differentially in determining the direction of arrow and gaze. Here, we address these questions by asking participants to perform a novel arrow-gaze Stroop task including arrow judgment task and gaze judgment task. We show that the congruency effect is ostensibly not affected by the upright or inverted faces in our modified Stroop task. Consistent with previous findings, we find that the magnitude of the congruency effect is larger for gaze than arrow judgment. By conducting a systematic hierarchical Bayesian estimation of three conflict drift-diffusion models (DDMs) – the diffusion model for conflict tasks (DMC), the dual-stage two-phase (DSTP) model and the shrinking spotlight (SSP) model, our study provides the first model-based assessment of holistic face processing-related cognitive control mechanisms. Fits of the models to data reveal a superiority of SSP over DMC and DSTP. The SSP accounts for our findings that 1) holistic face processing only affects the underlying factors in the arrow task instead of ostensible performance, however, part-based processing affects both levels in the gaze task; 2) both shared and dissociable attentional effects exist between eye gaze and arrow stimuli. These results provide valuable evidence of computational substrates in holistic face processing of cognitive control and in social & non-social attentional mechanisms.