This paper presents a numerical approach to simulate sliding friction between engineering surfaces with 3D roughness in point contacts. The numerical approach is developed on the basis of the deterministic solutions of mixed lubrication, which is able to predict the locations where the asperity contacts occur, and the pressure distribution over both lubrication and contact areas. If the friction coefficients over the contacting asperities have been determined, total friction force between the surfaces can be calculated by summing up the two components, i.e., the boundary friction contributed by contacting asperities and the shear stress in hydrodynamic regions. The frictions from asperity contact were determined in terms of a limiting shear stress or shear strength of boundary films while the fluid shear stress in the lubrication areas was calculated using different rheology models for the lubricant, in order to find which one would be more reliable in predicting fluid tractions. The simulations covered the entire lubrication, regime, including full-film Elastohydrodynamic Lubrication (EHL), mixed lubrication, and boundary lubrication. The results, when being plotted as a function of sliding velocity, give a Stribeck-type friction curve. This provides an opportunity to study friction change during the transition of lubrication conditions and to compare friction performance on different rough surfaces, which is of great value in engineering practice. Experiments were conducted on a commercial test device—universal material tester (UMT) to measure friction at a fixed load but different sliding velocities in reciprocal or rotary motions. The results also give rise to the Stribeck friction curves for different rough surfaces, which are to be compared with the results from simulations. The samples were prepared with typical machined surfaces in different roughness heights and textures, and in point contacts with steel ball. Results show that there is a general agreement between the experiments and simulations. It is found that surface features, such as roughness amplitude and patterns, may have a significant effect on the critical speed of transition from hydrodynamic to mixed lubrication. In the regime of mixed lubrication, rougher samples would give rise to a higher friction if the operation conditions are the same.