Satellite precipitation products (SPPs) have been widely evaluated at regional scales. However, there have been few quantitative comprehensive evaluations of SPPs using multiple indices. Ten high-resolution SPPs were quantitatively and comprehensively evaluated from precipitation occurrence and series indices using an improved rank score (RS) method in the data-scarce Qinghai–Tibetan Plateau (QTP). The new observation network, along with a number of national basic stations, was applied for SPP evaluation to obtain more reliable results. The results showed that the GPM and MSWEP showed the strongest overall performance, with an RS value of 0.75. CHIRPS and GPM had the strongest performance at measuring precipitation occurrence (RS = 0.92) and series (RS = 0.75), respectively. The optimal SPPs varied in evaluation indices, but also concentrated in the MSWEP, GPM, and CHIRPS. The bias of SPPs was markedly in the QTP, with relative error generally between −80% and 80%. In general, most SPPs showed the ability to detect precipitation occurrence. However, the SPPs showed relatively weak performance at measuring precipitation series. The mean Kling–Gupta efficiency of all stations was <0.50 for each SPP. The SPPs showed better performance in monsoon-affected regions, which mainly include the Yangtze, Yellow, Nu–Salween, Lancang–Mekong, Yarlung Zangbo–Bramaputra, and Ganges river basins. Performance was relatively poor in the westerly circulation areas, which mainly include the Tarim, Indus, and QTP inland river basins. The performance of SPPs showed a seasonal pattern during the year for most occurrence indices. The performance of SPPs in different periods was opposite in different indices. Therefore, multiple indices representing different characteristics are recommended for the evaluation of SPPs to obtain a comprehensive evaluation result. Overall, SPP measurement over the QTP needs further improvement, especially with regard to measuring precipitation series. The proposed improved RS method can also potentially be applied for comprehensive evaluation of other products and models.