It is well established that orbital scale sea-level changes generated larger transport of sediments into the deep-sea during the last glacial maximum than the Holocene. However, the response of sedimentary processes to abrupt millennial-scale climate variability is rather unknown. Frequency of distal turbidites and amounts of advected detrital carbonate are estimated off the Lisbon–Setúbal canyons (core MD03-2698, at 4602 mwd), within a chronostratigraphy based on radiometric ages, oxygen isotopes and paleomagnetic key global anomalies. We found that: 1) higher frequency of turbidites concurred with Northern Hemisphere coldest temperatures (Greenland Stadials [GS], including Heinrich [H] events). But more than that, an escalating frequency of turbidites starts with the onset of global sea-level rising (and warming in Antarctica) and culminates during H events, at the time when rising is still in its early-mid stage, and the Atlantic Meridional Overturning Circulation (AMOC) is re-starting. This short time span coincides with maximum gradients of ocean surface and bottom temperatures between GS and Antarctic warmings (Antarctic Isotope Maximum; AIM 17, 14, 12, 8, 4, 2) and rapid sea-level rises. 2) Trigger of turbidity currents is not the only sedimentary process responding to millennial variability; land-detrital carbonate (with a very negative bulk δ18O signature) enters the deep-sea by density-driven slope lateral advection, accordingly during GS. 3) Possible mechanisms to create slope instability on the Portuguese continental margin are sea-level variations as small as 20 m, and slope friction by rapid deep and intermediate re-accommodation of water masses circulation. 4) Common forcing mechanisms appear to drive slope instability at both millennial and orbital scales.