Phase evolution during the selenization is crucial for high-quality kesterite Cu2ZnSn(S, Se)4 (CZTSSe) absorbers and efficient solar cells. Herein, we regulate kinetic process of phase evolution from Cu+-Sn4+-MOE (MOE: 2-methoxyethanol) system by precisely controlling positive chamber pressure. We found that, at the heating-up stage, Se vapor concentration is intentionally suppressed in low-temperature region, which effectively reduces collision probability between the CZTS and Se atoms, thus remarkably inhibiting formation of secondary phases on the surface and multiple-step phase evolution processes. This strategy enables the phase evolution to start at relatively higher temperature and thereby leading to high crystalline quality CZTSSe absorber with fewer defects, and corresponding CZTSSe solar cell can present 14.1% efficiency (total area), which is the highest result so far. This work provides important insights into selenization mechanism of CZTSSe absorbers and explores a new way of kinetic regulation strategy to simplify the phase evolution path to efficient CZTSSe solar cells.