Kawasaki Disease (KD) is a rare febrile illness affecting infants and young children, potentially leading to coronary artery complications and, in severe cases, mortality if untreated. However, KD is frequently misdiagnosed as a common fever in clinical settings, and the inherent data imbalance further complicates accurate prediction when using traditional machine learning and statistical methods. This paper introduces two advanced approaches to address these challenges, enhancing prediction accuracy and generalizability. The first approach proposes a stacking model termed the Disease Classifier (DC), specifically designed to recognize minority class samples within imbalanced datasets, thereby mitigating the bias commonly observed in traditional models toward the majority class. Secondly, we introduce a combined model, the Disease Classifier with CTGAN (CTGAN-DC), which integrates DC with Conditional Tabular Generative Adversarial Network (CTGAN) technology to improve data balance and predictive performance further. Utilizing CTGAN-based oversampling techniques, this model retains the original data characteristics of KD while expanding data diversity. This effectively balances positive and negative KD samples, significantly reducing model bias toward the majority class and enhancing both predictive accuracy and generalizability. Experimental evaluations indicate substantial performance gains, with the DC and CTGAN-DC models achieving notably higher predictive accuracy than individual machine learning models. Specifically, the DC model achieves sensitivity and specificity rates of 95%, while the CTGAN-DC model achieves 95% sensitivity and 97% specificity, demonstrating superior recognition capability. Furthermore, both models exhibit strong generalizability across diverse KD datasets, particularly the CTGAN-DC model, which surpasses the JAMA model with a 3% increase in sensitivity and a 95% improvement in generalization sensitivity and specificity, effectively resolving the model collapse issue observed in the JAMA model. In sum, the proposed DC and CTGAN-DC architectures demonstrate robust generalizability across multiple KD datasets from various healthcare institutions and significantly outperform other models, including XGBoost. These findings lay a solid foundation for advancing disease prediction in the context of imbalanced medical data.