In software engineering, deep learning models are increasingly deployed for critical tasks such as bug detection and code review. However, overfitting remains a challenge that affects the quality, reliability, and trustworthiness of software systems that utilize deep learning models. Overfitting can be (1) prevented (e.g., using dropout or early stopping) or (2) detected in a trained model (e.g., using correlation-based approaches). Both overfitting detection and prevention approaches that are currently used have constraints (e.g., requiring modification of the model structure, and high computing resources). In this paper, we propose a simple, yet powerful approach that can both detect and prevent overfitting based on the training history (i.e., validation losses). Our approach first trains a time series classifier on training histories of overfit models. This classifier is then used to detect if a trained model is overfit. In addition, our trained classifier can be used to prevent overfitting by identifying the optimal point to stop a model's training. We evaluate our approach on its ability to identify and prevent overfitting in real-world samples. We compare our approach against correlation-based detection approaches and the most commonly used prevention approach (i.e., early stopping). Our approach achieves an F1 score of 0.91 which is at least 5% higher than the current best-performing non-intrusive overfitting detection approach. Furthermore, our approach can stop training to avoid overfitting at least 32% of the times earlier than early stopping and has the same or a better rate of returning the best model.