A systematic diagrammatic expansion for Gutzwiller-wave functions (DE-GWF) is formulated and used for the description of superconducting (SC) ground state in the two-dimensional Hubbard model with electron-transfer amplitudes t (and ) between nearest (and next-nearest) neighbors. The method is numerically very efficient and allows for a detailed analysis of the phase diagram as a function of all relevant parameters (U, ) and a determination of the kinetic-energy driven pairing region. SC states appear only for substantial interactions, , and for not too large hole doping, for =0.25t; this upper critical doping value agrees well with experiment for the cuprate high-temperature superconductors. We also obtain other important features of the SC state: (i) the SC gap at the Fermi surface resembles -wave only around the optimal doping and the corrections to this state are shown to arise from the longer range of the pairing; (ii) the nodal Fermi velocity is almost constant as a function of doping and agrees quantitatively with the experimental results; (iii) the SC transition is driven by the kinetic-energy lowering for low doping and strong interactions.