Triple-negative breast cancer (TNBC) is one of the most lethal subtypes of breast cancer (BC), and it accounts for approximately 10%–20% of all invasive BCs diagnosed worldwide. The survival rate of TNBC in stages III and IV is very low, and a large number of patients are diagnosed in these stages. Therefore, the purpose of this study was to identify TNBC-causing molecular signatures and anti-TNBC drug agents for early diagnosis and therapies. Five microarray datasets that contained 304 TNBC and 109 control samples were collected from the Gene Expression Omnibus (GEO) database, and RNA-Seq data with 116 tumor and 124 normal samples were collected from TCGA database to identify differentially expressed genes (DEGs) between TNBC and control samples. A total of 64 DEGs were identified, of which 29 were upregulated and 35 were downregulated, by using the statistical limma R-package. Among them, seven key genes (KGs) were commonly selected from microarray and RNA-Seq data based on the high degree of connectivity through PPI (protein–protein interaction) and module analysis. Out of these seven KGs, six KGs (TOP2A, BIRC5, AURKB, ACTB, ASPM, and BUB1B) were upregulated and one (EGFR) was downregulated. We also investigated their differential expression patterns with different subtypes and progression stages of BC by the independent datasets of RNA-seq profiles from UALCAN database, which indicated that they may be potential biomarkers for early diagnosis. Gene Ontology (GO) and the Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway enrichment analyses with the proposed DEGs were performed using the online Enrichr database to investigate the pathogenetic processes of TNBC highlighting KGs. Then, we performed gene regulatory network analysis and identified three transcriptional (SOX2, E2F4, and KDM5B) and three post-transcriptional (hsa-mir-1-3p, hsa-mir-124-3p, and hsa-mir-34a-5p) regulators of KGs. Finally, we proposed five KG-guided repurposable drug molecules (imatinib, regorafenib, pazopanib, teniposide, and dexrazoxane) for TNBC through network pharmacology and molecular docking analyses. These drug molecules also showed significant binding performance with some cancer-related PTM-sites (phosphorylation, succinylation, and ubiquitination) of top-ranked four key proteins (EGFR, AURKB, BIRC5, and TOP2A). Therefore, the findings of this computational study may play a vital role in early diagnosis and therapies against TNBC by wet-lab validation.