Classifying noisy data streams presents significant challenges due to the intertwined effects of attribute noise and label noise, which are rarely addressed simultaneously in existing methods. While concept drift and noise handling are critical in data stream learning, prior works often neglect the joint impact of attribute and label noise, leading to degraded model performance. In this paper, we propose ECIFC (Ensemble Classifier via Integration of Filter and Correction), a simple yet robust framework that tackles both attribute and label noise in a unified manner. Unlike complex approaches, ECIFC integrates noise filtering, label correction, and ensemble learning into a single framework with theoretical guarantees. To demonstrate the effectiveness of our method, we simply use the EM algorithm to estimate attribute and label log probabilities, use K-means to automatically determine noise thresholds, and derive ensemble classifier weights. Crucially, we rigorously prove the convergence of ECIFC, ensuring its stability in dynamic environments. Experiments on synthetic and real-world data streams demonstrate that ECIFC effectively identifies and mitigates both types of noise, achieving superior classification accuracy compared to state-of-the-art methods. The simplicity of our framework, combined with its theoretical foundation and empirical efficacy, makes ECIFC a practical and scalable solution for real-world noisy data stream classification.