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Ecological security and ecosystem stability in Central Asia depend heavily on the local vegetation. Vegetation dynamics and the response and hysteresis relationships to climate factors and drought on multiple scales over long time series in the region still need to be further explored. Using the net primary productivity (NPP) values as the vegetation change index of interest, in this study, we analyzed vegetation dynamics in Central Asia from 1982 to 2020 and assessed the responses and time lags of vegetation to climate factors and drought. The results showed that NPP gradually decreased from north to south and from east to west. Vegetation was distributed along both sides of the mountains. The temperatures rose from northeast to southwest, while precipitation gradually increased from southwest to northeast. The proportion of dry and wet years was as follows: normal (56.41%) slightly dry (28.2%) slightly humid (15.39%). Precipitation and drought conditions were positively correlated with NPP during the growing season, while temperature was negatively correlated with NPP. Increased spring temperature, precipitation, and drought conditions positively affected vegetation, while sustained summer temperature resulted in suppressed vegetation growth. Autumn vegetation was positively affected by temperature and drought, and precipitation was negatively correlated with autumn vegetation. Increasing winter temperatures promoted vegetation growth. The time lag between NPP and temperature gradually increased from northeast to southwest, and the time lag between NPP and precipitation gradually increased from south to north. Spring temperatures had the greatest beneficial impact on forestlands; summer climatic factors and drought had little effect on shrublands; the autumn climate exhibited small differences in its influence of each plant type; and winter temperatures had the greatest positive effect on grasslands. No time lag effect was found between any of the four vegetation types and precipitation. A one-month lag was found between cultivated lands and temperature; a two-month lag was found between forestlands and temperature; and a one-month lag was found between forestlands and drought and between shrublands and drought. The results can provide a scientific foundation for the sustainable development and management of ecosystems.