Cooperative events requiring anomalously large fluctuations are a defining characteristic for the onset of glassy relaxation across many materials. The importance of such intermittent events has been noted in systems as diverse as superconductors, metallic glasses, gels, colloids, and granular piles. Here, we show that prohibiting the attainment of new record-high energy fluctuations -- by explicitly imposing a ``lid on the fluctuation spectrum -- impedes further relaxation in the glassy phase. This lid allows us to directly measure the impact of record events on the evolving system in extensive simulations of aging in such vastly distinct glass formers as spin glasses and tapped granular piles. Interpreting our results in terms of a dynamics of records succeeds in explaining the ubiquity of both, the logarithmic decay of the energy and the memory effects encoded in the scaling of two-time correlation functions of aging systems.
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