Lung cancer is responsible for many deaths from cancer around the globe, primarily because it is difficult to find malignant lung nodules early enough to be treatable. We developed a hybrid deep learning approach to the automated classification of lung nodules from chest computed tomography (CT) images. Our model uses convolutional neural networks (CNNs) for hierarchical feature extraction, an attention mechanism for feature refinement in targeted regions of interest, and a support vector machine (SVM) classifier for robust margin-based decision making. Furthermore, we use a patch-based learning strategy within the model to improve sensitivity to small and ambiguous lung nodules. The model is tested on the publicly available LIDC-IDRI dataset and achieves 94.2% accuracy, 95.1% recall, and an area under the receiver operating characteristic curve (AUC-ROC) score of 0.971, which outperforms multiple baseline deep learning methods. The proposed method provides a synergistic integration of attention-weighted feature enhancements and traditional machine learning classifications as compared to traditional end-to-end architectures, resulting in improved model generalization and interpretability. Grad-CAM visualizations are also used to provide qualitative insights into the model decision-making process. The proposed hybrid approach provides a novel and interpretable solution for the classification of lung nodules from CT images that may assist in the development of computerized systems to assist physicians in making diagnoses using medical images.