Future projections of the Sahel rainfall are highly uncertain, with different climate models showing widely differing rainfall trends. Moreover, the twentieth-century cross-model consensus linking Sahel rainfall to tropical sea-surface temperatures (SSTs) is no longer applicable in the twenty-first century. Here we show that the diverse future Northern Hemisphere differential warming between extratropical and tropical SSTs can explain the discrepancy in the projected Sahel rainfall. The relationship between SST and Sahel rainfall that holds for the twentieth-century persists into the twenty-first century when the differential SST warming is taken into account. A suite of SST-sensitivity experiments confirms that strong Northern Hemisphere extratropical warming induces a significant increase in Sahel rainfall, which can predominate over the drying impact of tropical SST warming. These results indicate that a trustworthy projection of Sahel rainfall requires the estimation of the most likely future Northern-hemispheric differential warming.