Stellar classification, a fundamental aspect of astronomy, offers a structured approach to comprehend and characterize the vast diversity of celestial entities. Here we present a new fine-tuned deep convolutional neural network of 1D separable convolutional blocks for stellar classification based on spectral properties using SSDS-17 data from the Sloan Digital Sky Survey, where class imbalance is evaluated using the MIN class and SMOTE balancing techniques. The results obtained during the performance evaluation confirmed the reliability of the proposed architecture of StellarNet in multi-class stellar classification, achieving remarkable values of about 97% and 99% for accuracy and AUC score, respectively. The proposed StellarNet architecture has been used in a real-time streaming processing pipeline that includes a streaming learning functionality that can be deployed in observatories and related centers to perform the real-time labeling and sorting of the captured data.