Sulfur(VI) fluoride exchange reactions have been applied to the linkage of a diverse range of molecules. However, the connectivity of fluorosulfuryls with alkynes remains a formidable challenge owing to the high reactivity of π systems. Here, we report a divergent sulfur(VI) fluoride exchange reaction between sulfonimidoyl fluorides and alkynes to afford vinylic and acetylenic sulfoximines. Experimental and computational mechanistic studies elucidated key BF3-bridged six-membered transition states that enabled the synchronous activation of silicon-capped alkynes and sulfonimidoyl fluorides via the interactions of F···Si and B···F. Mechanistic studies also revealed that N-benzyl sulfonimidoyls undergo a 1,5-hydrogen migration from the benzylic position to the acetylenic position, which generates the observed vinylic sulfoximines. A range of synthetic transformations, which include azide–alkyne cycloadditions were demonstrated on the vinylic and acetylenic sulfoximine products.