Hypertension is one of the most important chronic diseases worldwide. Hypertension is a critical condition encountered frequently in daily life, forming a significant area of service in Primary Health Care (PHC), which healthcare professionals often confront. It serves as a precursor to many critical illnesses and can lead to fatalities if not addressed promptly. Our study underscores the importance of this critical issue by analyzing articles related to hypertension in the PHC research area from the Web of Science Core Collection using bibliometric methods and machine learning techniques, specifically topic analyses using the latent Dirichlet allocation method. The analysis was conducted using Python Scikit-learn, Gensim, and Wordcloud Libraries, the VosViewer program, and the Bibliometrix R Biblioshiny library. Our findings revealed a steady increase in publication output in hypertension-related research. Analysis shows that hypertension-related research in the PHC research area is clustered into 8 groups: (1) management of hypertension in PHC, risk factors, and complications; (2) psychiatric disorders and hypertension; (3) pediatric and pregnancy hypertension; (4) environmental factors and living conditions; (5) sex and age effects on hypertension; (6) COVID-19 and hypertension; (7) behavioral risk factors, quality of life, and awareness; and (8) current treatment methods and guidelines. Research on hypertension has focused intensively on kidney disease, obesity, pregnancy, cardiovascular risk, heart disease, calcium channel blockers, body mass index, amlodipine, mortality, risk factors, hyperlipidemia, depression, and resistant hypertension. This study represents the first and comprehensive bibliometric analysis of hypertension in the PHC research area. Annual publication volumes have steadily increased over the years. In recent years, topics such as social determinants, patient attendance, self-management, diabetes mellitus, COVID-19, telemedicine, type 2 diabetes, and noncommunicable diseases have garnered significant interest in the field of PHC services.