Due to the n(N)-to-pi*(C & boxH;O) conjugation, the direct functionalization of unactivated amides via C-N activation is a longstanding challenge in functional group interconversion involving ubiquitous amide linkages. Herein, we report highly chemoselective esterification of unactivated tertiary amides with various equivalent oxygen nucleophiles, including both aliphatic alcohols and weakly nucleophilic phenols, for the first time. In this reaction, amide C-N bonds are electrophilically activated through cooperative acid/iodide catalysis via the selective formation of a highly reactive acyl iodide species. This powerful strategy enables the use of a stoichiometric quantity of O-H nucleophiles and provides the first general method for converting unactivated N,N-dialkyl amides into the corresponding esters with exquisite chemoselectivity. An exceptionally wide substrate scope of both amides and oxygen nucleophiles is demonstrated with high functional group tolerance, including the late-stage modification of some drugs' amide derivatives and bioactive O-H nucleophiles (>100 examples). We anticipate that this powerful esterification of amides will find wide application in synthetic organic chemistry.