We described an integrated-fin gasket technique for the palm cubic-anvil apparatus specialized for the high-pressure and low-temperature measurements. By using such a gasket made from the semi-sintered MgO ceramics and the tungsten-carbide anvils of 2.5 mm square top, we successfully generate pressures over 16 GPa at both room and cryogenic temperatures down to 0.5 K. We observed a pressure self-increment for this specific configuration and further characterized the thermally induced pressure variation by monitoring the antiferromagnetic transition temperature of chromium up to 12 GPa. In addition to enlarge the pressure capacity, such a modified gasket also improves greatly the surviving rate of electrical leads hanging the sample inside a Teflon capsule filled with the liquid pressure-transmitting medium. These improvements should be attributed to the reduced extrusion of gasket materials during the initial compression.