Precipitation extremes have important implications for regional water resources and ecological environment in endorheic (landlocked) basins. The Hongjian Lake Basin (HJLB), as the representative inflow area in the Ordos Plateau in China, is suffering from water scarcity and an ecosystem crisis; however, previous studies have paid little attention to changes in precipitation extremes in the HJLB. In this study, we investigated the spatio-temporal variations of the core extreme precipitation indices (i.e., PRCTOT, R99p, Rx1day, Rx5day, SDII, R1, R10, CWD, and CDD) recommended by the Expert Team on Climate Change Detection and Indices (ETCCDI), and analyzed the climatic dry–wet regime indicated by these extreme indices during 1960–2014 in the HJLB. The results show that the nine extreme indices had large differences in temporal and spatial variation characteristics. All the nine extreme precipitation indices showed a large fluctuation, both in the whole period and in the three detected different sub-periods, with variation magnitudes of 13%–52%. Most extreme indices had non-significant downward trends, while only the consecutive wet days (CWD) had a significant upward trend. The eight extreme wet indices increased from northwest to southeast, while the consecutive dry days (CDD) had the opposite change direction. Each index had a different trend with different spatial distribution locations and areas. The nine extreme indices revealed that the climate in the HJLB has become a drought since the early 1980s. This was specifically indicated by all four extreme precipitation quantity indices (PRCTOT, R99p, Rx1day, Rx5day) and the extreme intensity index (SDII) declining, as well as the number of heavy precipitation days (R10) decreasing. When the dry–wet variations was divided into the different sub-periods, the climatic dry–wet changes of each index demonstrated more inconsistency and complexity, but most indices in the first sub-period from 1960 to the late 1970s could be regarded as a wet high-oscillation phase, the second sub-period after the early 1980s was a relatively dry low-oscillation phase, and the third sub-period after the late 1990s or early 21st century was a dry medium-oscillation phase. It is worth noting that most extreme indices had an obvious positive linear trend in the third sub-period, which means that in the last 20 years, the precipitation extremes showed an increasing trend. This study could provide a certain scientific reference for regional climate change detection, water resources management, and disaster prevention in the HJLB and similar endorheic basins or inland arid regions.