The characteristics of surface morphology markedly affect the tribological properties of contact interface such as lubrication and seal performance. In present work, the synergetic effect of surface connectivity and some three-dimensional topography parameters (ISO 25178) on the friction characteristics of a sliding contact interface, based on mathematical morphology and reciprocating linear tribotesting, is explored. The results indicate that the friction properties of sliding contact interface was significantly affected by the variation of surface connectivity. The increase in connectivity index would improve the relative contact area on the isotropic surfaces and affect the distribution and storage characteristics of the fluid, while this enhancement would be blocked on the anisotropic surface and the variation of connectivity index is obviously nonlinear with a shocking feature. The friction tests confirm that the friction coefficient of sliding contact interface decreases with the increasing surface connectivity index, which is mainly related to the enhancement of lubricant storage and flow in each void region and improving the lubrication behavior. Furthermore, the same variation law is applicable to the relationship between the functional morphology parameters and the friction property. The increasing Vvv and Sku, would contribute to a lower friction coefficient at the interface. Our work provides deep insights into regulating the tribological property of contact interfaces through surface topography control.