Potato (Solanum tuberosum) is the third and fourth most important tuberous crop in terms of human consumption and production, respectively. However, its growth and development are affected by drought, which is an emerging threat to agriculture especially in arid and semiarid areas. Potassium (K) is a well-known macronutrient that improves the performance of crops under drought. Therefore, the present study was enacted with the aim of evaluating the impact of K fertilizer on potato crop growth, productivity, and drought tolerance under full root irrigation (FRI) and partial root irrigation (PRI) conditions. Two potato cultivars (Lady Rosetta and Hermes) were grown under normal field conditions followed by FRI and PRI applications. Potassium sulfate was applied in three doses (T0 = 50 kg·ha−1, T1 = 75 kg·ha−1, and T2 = 100 kg·ha−1). The experiment was laid out under randomized complete block design (RCBD) with split plot arrangement. The main plot was allocated to irrigation, along with a subplot to potassium and a sub-subplot to potato cultivars. The results indicated that K application significantly improved the plant growth and yield by exhibiting better performance in morpho-physiological and biochemical attributes under FRI and PRI conditions; however, a more remarkable change was noticed under PRI compared with FRI. K application alleviated drought stress regardless of cultivars. This study suggests that K application at the rate of 100 kg·ha−1 is an effective approach for inducing drought tolerance in potato crops.