For detection of incipient faults in power transformers, this paper presents three implementations of a hybrid binary multistage classification (BMC) technique using different AI methodologies—Adaptive Neuro Fuzzy Inference System (ANFIS), Artificial Neural Networks (ANN), and Support Vector Machine (SVM). The classification method integrates established Dissolved Gas Analysis (DGA) ratio methods, including Roger’s ratio method, IEC 60,599 method, and Doernenburg’s method, in a multistage, binary approach for fault diagnosis, aiming for higher accuracy. The classification process begins by determining the presence or absence of faults and then progresses to identify the type and severity of faults in subsequent stages. Separate intelligent models using ANFIS, ANN, and SVM are developed for each DGA method and classification stage. Following a detailed stage-by-stage comparison, a hybrid diagnostic model is constructed, selecting the most accurate DGA-based binary classifiers for each stage. A comparative analysis is performed to determine the effectiveness of each AI methodology. The results highlight the superiority of SVM as the most accurate binary classification technique compared to ANN and ANFIS in diagnosing faults in power transformers.