Stress became a common factor in the busy daily routines of all academic and corporate working environments. Everyone checks for efficient stress-buster alternatives to calm down from work pressure. Instead of investing time in unnecessary efforts, this work shows the stress relief scenario of subjects by listening to “Raag Darbari” music notes as a simple add-on to their schedule. An innovative approach has been implemented on the “MUSEI-EEG” dataset using Topological Data Analysis (TDA) to analyze this stress relief study. This study reveals that persistent homological features can be robust biomarkers for classifying closely distributed subject data. The proposed TDA approach framework revealed homological features like birth-death rate and entropy efficacy in stress prediction using Electroencephalogram (EEG) signals with 86% average accuracy and 0.2 standard deviation.