The aging behaviour of dense suspensions or pastes at rest is almost exclusively attributed to structural dynamics. Here, we identify another aging process, contact-controlled aging, consisting in the progressive stiffening of solid-solid contacts, after their initial formation rapidly arrests the microstructure. By combining rheometry, confocal microscopy, and particle-scale mechanical tests using laser tweezers, we demonstrate that this process governs the shear modulus aging of dense aqueous silica and polymer latex suspensions at moderate ionic strengths. We further show that contact-controlled aging becomes relevant as soon as Coulombic interactions are sufficiently screened out that the formation of solid-solid contacts is not limited by activation barriers. Given that this condition only requires moderate ion concentrations, contact-controlled aging should be generic in a wide class of materials, such as cements, soils, or 3D inks, thus questioning our understanding of aging dynamics in these systems.