In this article a new method is presented to obtain a full and precise calibration of camera-robot systems with eye-in-hand cameras. It achieves a simultaneous and numerically stable calibration of intrinsic and extrinsic camera parameters by analysing the image coordinates of a single point marker placed in the environment of the robot. The method works by first determining a rough initial estimate of the camera pose in the tool coordinate frame. This estimate is then used to generate a set of uniformly distributed calibration poses from which the object is visible. The measurements obtained in these poses are then used to obtain the exact parameters with CMA-ES (Covariance Matrix Adaptation Evolution Strategy), a derandomised variant of an evolution strategy optimiser. Minimal claims on the surrounding area and flexible handling of environmental and kinematic limitations make this method applicable to a range of robot setups and camera models. The algorithm runs autonomously without supervision and does not need manual adjustments. Our problem formulation is directly in the 3D space which helps in minimising the resulting calibration errors in the robot's task space. Both simulations and experimental results with a real robot show a very good convergence and high repeatability of calibration results without requiring user-supplied initial estimates of the calibration parameters.