We developed a real-time sleep stage classification system with a convolutional neural network using only a one-channel electro-encephalogram source from mice and universally available features in any time-series data: raw signal, spectrum, and zeitgeber time. To accommodate historical information from each subject, we included a long short-term memory recurrent neural network in combination with the universal features. The resulting system (UTSN-L) achieved 90% overall accuracy and 81% multi-class Matthews Correlation Coefficient, with particularly high-quality judgements for rapid eye movement sleep (91% sensitivity and 98% specificity). This system can enable automatic real-time interventions during rapid eye movement sleep, which has been difficult due to its relatively low abundance and short duration. Further, it eliminates the need for ordinal pre-calibration, electromyogram recording, and manual classification and thus is scalable. The code is open-source with a graphical user interface and closed feedback loop capability, making it easily adaptable to a wide variety of end-user needs. By allowing large-scale, automatic, and real-time sleep stage-specific interventions, this system can aid further investigations of the functions of sleep and the development of new therapeutic strategies for sleep-related disorders.