Non-pharmaceutical interventions (NPIs) and vaccination are two fundamental approaches to mitigate the coronavirus disease 2019 (Covid-19) pandemic. Vaccination strategies are generally less costly and socially/economically disruptive than NPI strategies, such as business closures, social distancing, and face mask mandates, as evidenced by highly vaccinated countries generally rolling back NPIs. However, the respective real-world impact of an NPI strategy versus vaccination strategy, or the combination of both, on mitigating Covid-19 transmission remains uncertain. To address this, we built a Bayesian inference model to explore the changing effectiveness of NPIs and vaccination based on the assembled large-scale dataset, including epidemiological parameters, variants, vaccines, and control variable. Here we show that NPIs were still considerably complementary or even synergistic to vaccination in the effort to curb the Covid-19 infection before reaching herd immunity. We found that (1) the synergistic effect of NPIs and vaccination was 46.9% (reduction in reproduction number) in September 2021, whereas the effects of NPIs and vaccination alone were 20.7% and 28.8%, respectively; (2) effectiveness of NPIs is less sensitive to emerging COVID-19 variants but decreases with vaccination progress, as NPIs may unnecessarily restrict the vaccinated population. The effectiveness of NPIs alone declined approximately 23% since the introduction of vaccination strategies, where the relaxation of NPIs promoted the decline from May 2021. Our results demonstrate that the decision to relax NPIs should consider the real-world vaccination rate of the relevant population, which is determined by the observed vaccine efficacy in relation to extant and emerging variants.