This article discusses experimental results concerning the quality of through holes drilled in Inconel 718. The tests involved hole cutting under 27 different conditions using different values of the feed per revolution and spindle speed, and different types of kinematic system. The drilling was performed on a CTX Alpha 500 universal turning center using tools with internal coolant supply. Three kinematic systems were considered for hole cutting. The first, based on the driven tool holder, had a stationary workpiece and a rotating and linearly fed tool. In the second, where drilling was based on the spindle rotations, the workpiece rotated while the tool moved along a straight line. In the third system, the workpiece and the tool rotated in opposite directions; the tool also performed a linear motion. The study aimed to assess the quality of holes on the basis of the following output parameters: the hole diameter, cylindricity and straightness errors, and the surface texture. A multifactorial statistical analysis was used to determine how the hole quality was dependent on the process parameters and the type of drilling kinematics. The findings confirm that the kinematic system, as well as the feed per revolution, are the key factors affecting the quality of holes drilled in Inconel 718. The analysis of the hole drilling process for Inconel 718, performed using a CNC turning center, shows that the third kinematic system was the best option as all the four parameters describing the hole quality had the lowest values. The best results were obtained in the 6th (n = 637 rpm, fn = 0.075 mm/rev, KIN III) and 8th experiments (n = 955 rpm, fn = 0.075 mm/rev, KIN II), because the parameters were then the lowest, with the scatter of results being up to 30%.