Schwartz’s reagent, Cp$_2$Zr(H)Cl, has traditionally been used as a stoichiometric reagent for the reduction of unsaturated organic molecules. Recently, methods to use Cp$_2$Zr(H)Cl as a catalyst have been developed through turnover of the Zr–X intermediates, formed upon reaction with an organic substrate, with hydride reagents. Herein, we report the development of a new catalytic pathway for the reduction of esters that uses the bench-stable silane Me(OMe)$_2$SiH (DMMS) as a mild stoichiometric reductant and Cp$_2$Zr(H)Cl as the catalyst. This system exploits the regeneration of Zr–H through the sigma bond metathesis of Zr–O and Si–H to achieve catalyst turnover. These reaction conditions tolerate a range of reducible functional groups (e.g. alkyne, alkene, and nitro) and give high yields of the corresponding alcohol (up to 91% isolated yield). We have also applied this methodology to the reductive depolymerisation of polyesters found in household plastic waste.