Existing research combines acupuncture theory with network science and proposes a new paradigm for the study of acupoint selection patterns—a key acupoint mining algorithm based on acupoint networks. However, the basic idea of this study for finding key acupoints is based on binary acupoint synergy relationships, which ignores the higher-order synergy among multiple acupoints and does not truly reflect the implicit patterns of each acupoint among meridian systems. Moreover, the mining results assessment method, which this new paradigm involves, does not have wide applicability and universality. In this paper, with the introduction of higher-order interactions between multiple acupoints, a high-specificity key acupoint mining algorithm based on 3-node motif is proposed in the acupoint-disease network (ADN). In response to the narrow applicability of the new research paradigm involving the evaluation of algorithms’ measures, new and widely applicable and universal evaluation criteria are introduced in terms of resolution, network loss, and accuracy, respectively. Based on the principles of acupoint selection involved in acupuncture clinics in Chinese medicine, the acupoints involved in the data were divided into a total of 19 regions according to their distribution characteristics. From these 19 regions, we selected the key acupoints that have a large impact on the global network. Finally, we compared this algorithm with five other acupoint importance assessment algorithms in terms of resolution, network loss, and accuracy, respectively. The comprehensive results show that the algorithm identifies key acupoints with an accuracy of 63%, which is 14% to 21% higher than other existing methods. The key acupoints identified by the algorithm have a significant disruptive effect on the connectivity of the network, indicating that the key acupoints are at the core of the acupoint-disease network topology. They have a significant propagation influence on other acupoints, which means that the key acupoints have high-synergistic cooperation with other acupoints. Meanwhile, the stability and specificity of the algorithm ensure the reliability of the key acupoints. We believe that the key acupoints identified by the algorithm can be used as core acupoints from the perspective of network topology and high synergy of other acupoints, respectively, and help researchers explore targeted and high-impact combinations of acupoints to optimize existing acupuncture prescriptions under condition constraints.