Screw withdrawal resistance (SWR) is a metric that assesses the strength of furniture joints made with wood screws. The SWR value is influenced by several factors, such as the size of the screw, the depth to which it is embedded, the diameter of the pilot hole, and the material properties of the furniture components that are being joined together. These factors have been widely studied in the scientific literature. The objective of the research was to investigate the previously unexplored factor of a feed rate during pilot hole drilling and its influence on SWR. This study used three particleboards composed of raw pine material and urea–formaldehyde resins; the boards varied in average density (633, 637, and 714 kg/m3). Blind pilot holes with a diameter of 5 mm and depth of 25 mm were drilled in these boards using three significantly different feed rates (0.033, 0.33, and 3.33 mm/rev.). Subsequently, a confirmat-type furniture screw (7 mm major diameter, 4 mm minor diameter, 3 mm pitch) was screwed into these pilot holes. The ultimate SWR was measured with a universal testing machine. The results showed that the highest feed rate significantly decreases the SWR for all particleboards tested. This phenomenon can be attributed to the fact that a higher feed rate leads to a decreased precision in the internal surface of the pilot hole, consequently diminishing the screw’s anchoring capacity within the hole. The high feed rate, used to increase production efficiency, may significantly reduce furniture durability and usability.