With the rapid expansion of electric vehicles (EVs) and energy storage systems (ESS), ensuring the operational safety of lithium-ion batteries has become a critical technical challenge. Conventional battery management systems (BMS) primarily rely on threshold-based rule logic, which is limited in detecting coupled anomalies and early-stage degradation patterns. In this study, a deep learning-based framework for multivariate anomaly detection is proposed using BMS sensor data, including voltage, current, temperature, state of charge (SOC), and state of health (SOH). Five representative fault scenarios were defined, including thermal runaway precursors, cell voltage imbalance, SOC inconsistency, internal resistance increase, and communication delay. The proposed CNN-LSTM model was compared with conventional Rule-based methods and machine learning models, including Isolation Forest, Autoencoder, and LSTM. Experimental results show that the proposed model achieved the highest performance, with an F1-score of 0.885, an AUC of 0.94, and a detection delay of 8.1 s. In contrast, the Rule-based method exhibited a significantly higher false negative rate of 42.0%, indicating limitations in detecting complex anomaly patterns. These results demonstrate that the proposed spatiotemporal deep learning approach can significantly improve the accuracy and responsiveness of battery anomaly detection. Furthermore, the proposed method is expected to contribute to enhancing safety, reliability, and predictive diagnostics in next-generation intelligent BMS platforms.