Early diagnosis of incipient faults in power transformers enables their predictive maintenance and guarantees their proper operation. Recently, machine learning (ML) techniques have played special role in fault diagnosis in power transformers; however, the application of such data-driven methods has been hampered by the lack of quality data to support their learning process. Since the collection of dissolved gas analysis (DGA) data depends on equipment failures, the obtaining of large labeled datasets that characterize incipient faults is a difficult task. The use of over-sampling techniques can overcome this challenge by providing a synthetic dataset with balanced classes for the ML method’s learning process. This paper addresses a novel application of a deep neural network classifier for the diagnosis of a dataset enriched by the Borderline synthetic minority over-sampling method. The performance of the model was compared with those of traditional DGA interpretation methods, traditional multilayer percetron networks (MLP) and a DNN working with the original dataset. The results indicate the superiority of the approach, and a noise-resilience analysis conducted revealed its ability to deal with corrupted data. The methodology is of simple implementation, highly accurate, and capable of correctly classifying over 84% of the test samples.