Modern large language models increasingly require long contexts for reasoning and multi-document tasks, but attention’s quadratic complexity creates a severe computational bottleneck. We present Block Sparse Flash Attention (BSFA), a drop-in replacement that accelerates long-context inference while preserving model quality. Unlike methods that predict importance before computing scores, BSFA computes exact query-key similarities to select the top-k most important value blocks for each query. By comparing per-block maximum scores against calibrated thresholds, we skip approximately 50% of the computation and memory transfers for pruned blocks. Our training-free approach needs only a single calibration step on a small dataset to set the thresholds for each layer and head. We provide a CUDA kernel implementation that can be used as a drop-in replacement for FlashAttention. On Llama-3.1-8B, BSFA achieves up to 1.13× end-to-end speedup on LongBench with only a 1.1% accuracy drop, and up to 1.24× on Needle-in-a-Haystack retrieval at a 1% accuracy drop. The attention kernel itself accelerates by up to 1.38×. We compare BSFA against five recent sparse attention baselines (SpargeAttention, MInference, FlexPrefill, XAttention, and BLASST), and verify the method on Qwen2.5-7B and on A6000 and H100 GPUs. The implementation is available at https://github.com/Danielohayon/Block-Sparse-Flash-Attention.