Transfer learning typically leverages representations learned from a source domain to improve performance on a target task. A common approach is to extract features from a pre-trained model and directly apply them for target prediction. However, this strategy is prone to negative transfer where the source representation fails to align with the target distribution. In this article, we propose Residual Feature Integration (REFINE), a simple yet effective method designed to mitigate negative transfer. Our approach combines a fixed source-side representation with a trainable target-side encoder and fits a shallow neural network on the resulting joint representation, which adapts to the target domain while preserving transferable knowledge from the source domain. Theoretically, we prove that REFINE is sufficient to prevent negative transfer under mild conditions, and derive the generalization bound demonstrating its theoretical benefit. Empirically, we show that REFINE consistently enhances performance across diverse application and data modalities including vision, text, and tabular data, and outperforms numerous alternative solutions. Our method is lightweight, architecture-agnostic, and robust, making it a valuable addition to the existing transfer learning toolbox.