A novel formal cross-coupling of aryl methyl sulfones and alcohols affording alkyl aryl ethers via an SRN1 pathway is developed. Two marketed antitubercular drugs were efficiently prepared employing this approach as the key step. A dimsyl-anion initiated radical chain process was revealed as the major pathway. DFT calculations indicate that the formation of a radical anion via nucleophilic addition of alkoxide to the aryl radical is the key step in determining the observed chemoselectivity.