The Tarim Basin is located in an arid inland area; the ecological environment is fragile, and it is extremely sensitive to climate change. For the purpose of studying dynamic changes in the vegetation response of vegetation in the Tarim Basin to extreme climate, this study used the Vegetation Ecological Quality Index (EQI) as a vegetation indicator and calculated 12 extreme climate indices using Rclimdex. Pearson correlation analysis was used to explore the relationship between EQI values and various extreme climate indices at both inter-annual and intra-annual scales. Additionally, geographic detector analysis was employed to examine the single and interactive effects of extreme climate on the EQI for different vegetation types. The following was found: (1) During 2000–2022, the EQI showed an upward trend in the Tarim Basin, and the increase in agricultural vegetation was the fastest. (2) Since 2000, the extreme warm temperature indices have risen, whereas the extreme cold temperature indices have declined. The warming rate of nighttime temperatures exceeds that of daytime, and the extreme precipitation rises intensively. Simultaneously, continuous dry days have also increased. (3) On an inter-annual scale, the EQI is primarily negatively correlated with the most extreme warm temperature indices, while it is positively correlated with extreme cold temperatures and extreme precipitation indices. On an intra-annual scale, there is an obvious regional concentration in the correlation between the EQI and extreme climate indices. The diurnal temperature range (DTR) and cold daytimes (TX10P) have inhibitory and promoting effects on areas with high and low EQI, respectively. The extremum indices, temperature warm indices, and precipitation intensity indices have a promoting effect on areas with a high EQI and an inhibiting effect on areas with a low EQI. The interaction between extreme climate indices has a greater impact on the EQI than the effect of a single extreme climate index, especially with a significant impact on forests and shrubs. This study provides a reference for the early warning of meteorological disasters, ecosystem protection, and sustainable management in the Tarim Basin.