Online planning and execution of minimum-time maneuvers on three-dimensional (3D) circuits is an open challenge in autonomous vehicle racing. In this paper, we present an artificial race driver (ARD) to learn the vehicle dynamics, plan and execute minimum-time maneuvers on a 3D track. ARD integrates a novel kineto-dynamical (KD) vehicle model for trajectory planning with economic nonlinear model predictive control (E-NMPC). We use a high-fidelity vehicle simulator (VS) to compare the closed-loop ARD results with a minimum-lap-time optimal control problem (MLT-VS), solved offline with the same VS. Our ARD sets lap times close to the MLT-VS, and the new KD model outperforms a literature benchmark. Finally, we study the vehicle trajectories, to assess the re-planning capabilities of ARD under execution errors. A video with the main results is available as supplementary material.