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Geological sediment archives document a rich periodic series of astronomically driven climate, but record also abrupt, severe climatic changes called events, the multi-Myr boundary conditions of which have generally been ascribed to acyclic processes from Earth's interior dynamics. These events have rarely been considered together within extended time series for potential correlation with long-term (multi-million year, Myr) cycling. Here I show a coupling between events and multi-Myr cycles in a temperature and ice-volume climatic proxy of the geological past 115 Myr. I use Cenozoic through middle Cretaceous climatic variations, as recorded in benthic foraminifera delta O-18, to highlight prominent similar to 9 and similar to 36 Myr cyclicities. These cyclicities were previously attributed either to astronomical or tectonic variations. In particular, I point out that most of the well-known events during the past 115 Myr geological interval occur during extremes in the similar to 9 and similar to 36 Myr cycling. One exception is the early Cenozoic hyperthermal events including the salient Paleocene-Eocene Thermal Maximum (similar to 56 Ma), which do not match extremes in long-period cyclicities, but to inflection point of these cycles. Specific focus on climatic events, as inferred from delta O-18 proxy, suggest that some "events", marked by gradual trends within the similar to 9 and similar to 36 Myr cycle extremes, would principally be paced by long-term cycling, while "events", recorded as abrupt delta O-18 changes nearby cycle extremes, would be rather induced by acyclic processes. The connection between cyclic and acyclic processes, as triggers or feedbacks, is very likely. Such link between cycling and events in Earth's past climate provides insight into celestial dynamics governing perturbations in Earth's surface systems, but also the potential connection between external and Earth's interior processes.