The quadratic complexity of attention imposes severe memory and computational bottlenecks on Large Language Model (LLM) inference. This challenge is particularly acute for emerging agentic applications that require processing multi-million token sequences. We propose STS, a sparse attention mechanism that requires no model retraining. STS leverages the key insight that tokens identified as important by a smaller draft model are highly predictive of important tokens for a larger target model. By integrating into speculative decoding frameworks, STS repurposes the draft model's attention scores to dynamically construct a token-and-head-wise sparsity mask. This mask effectively prunes the expensive attention computation in the target LLM. Our evaluation shows that STS achieves a 2.67x speedup operating at approximately 90% sparsity on representative benchmark NarrativeQA, maintaining negligible accuracy degradation compared to dense attention. STS establishes a new state-of-the-art on the sparsity-accuracy trade-off, outperforming prior techniques by enabling higher sparsity levels for a given accuracy budget.