Changes in the magnitude of millennial-scale climate variability (MCV) during the Late Pleistocene occur as a function of changing background climate state over tens of thousands of years, an indirect consequence of slowly varying incoming solar radiation associated with changes in Earth’s orbit. However, whether astronomical forcing can stimulate MCV directly (without a change in the background state) remains to be determined. Here we use a comprehensive fully coupled climate model to demonstrate that orbitally driven insolation changes alone can give rise to spontaneous millennial-scale climate oscillations under intermediate glacial conditions. Our results demonstrate that an abrupt transition from warm interstadial to cold stadial conditions can be triggered directly by a precession-controlled increase in low-latitude boreal summer insolation and/or an obliquity-controlled decrease in high-latitude mean annual insolation, by modulating North Atlantic low-latitude hydroclimate and/or high-latitude sea ice–ocean–atmosphere interactions, respectively. Furthermore, contrasting insolation effects over the tropical versus subpolar North Atlantic, exerted by obliquity or precession, result in an oscillatory climate regime, even within an otherwise stable climate. With additional sensitivity experiments under different glacial–interglacial climate backgrounds, we synthesize a coherent theoretical framework for climate stability, elaborating the direct and indirect (dual) control by Earth’s orbital cycles on millennial-scale climate variability during the Pleistocene.