Large language models are increasingly capable of handling long-context inputs, but the memory overhead of KV cache remains a major bottleneck for general-purpose deployment. While many compression strategies have been explored, sequence-level compression is particularly challenging due to its tendency to lose important details. We present UniGist, a gist token-based long context compression framework that removes the need for chunk-wise training, enabling the model to learn how to compress and utilize long-range context during training. To fully exploit the sparsity, we introduce a gist shift trick that transforms the attention layout into a right-aligned block structure and develop a block-table-free sparse attention kernel based on it. UniGist further supports one-pass training and flexible chunk sizes during inference, allowing efficient and adaptive context processing. Experiments across multiple long-context tasks show that UniGist significantly improves compression quality, with especially strong performance in recalling details and long-range dependency modeling.