Heart failure with preserved ejection fraction (HFpEF) is a complex disease characterized by dysfunctions in the heart, adipose tissue, and cerebral arteries. The elucidation of the interactions between these three tissues in HFpEF will improve our understanding of the mechanism of HFpEF. In this study, we propose a multilevel comparative framework based on differentially expressed genes (DEGs) and differentially correlated gene pairs (DCGs) to investigate the shared and unique pathological features among the three tissues in HFpEF. At the network level, functional enrichment analysis revealed that the networks of the heart, adipose tissue, and cerebral arteries were enriched in the cell cycle and immune response. The networks of the heart and adipose tissues were enriched in hemostasis, G-protein coupled receptor (GPCR) ligand, and cancer-related pathway. The heart-specific networks were enriched in the inflammatory response and cardiac hypertrophy, while the adipose-tissue-specific networks were enriched in the response to peptides and regulation of cell adhesion. The cerebral-artery-specific networks were enriched in gene expression (transcription). At the module and gene levels, 5 housekeeping DEGs, 2 housekeeping DCGs, 6 modules of merged protein–protein interaction network, 5 tissue-specific hub genes, and 20 shared hub genes were identified through comparative analysis of tissue pairs. Furthermore, the therapeutic drugs for HFpEF-targeting these genes were examined using molecular docking. The combination of multitissue and multilevel comparative frameworks is a potential strategy for the discovery of effective therapy and personalized medicine for HFpEF.