Potato (Solanum tuberosum L.) tubers are a highly important food crop in many countries due to their nutritional value and health-promoting properties. Postharvest disease caused by Phytophthora infestans leads to the significant decay of stored potatoes. The main objective of this study was to evaluate the effects of the endophytic bacteria, Bacillus subtilis (strain 10–4), or its combination with salicylic acid (SA), on some resistance and quality traits of stored Ph. infestans-infected potato tubers. The experiments were conducted using hydroponically grown potato mini-tubers, infected prior to storage with Ph. infestans, and then coated with B. subtilis, alone and in combination with SA, which were then stored for six months. The results revealed that infection with Ph. infestans significantly increased tuber late blight incidence (up to 90–100%) and oxidative and osmotic damage (i.e., malondialdehyde and proline) in tubers. These phenomena were accompanied by a decrease in starch, reducing sugars (RS), and total dry matter (TDM) contents and an increase in amylase (AMY) activity. Moreover, total glycoalkaloids (GA) (α-solanine, α-chaconine) notably increased in infected tubers, exceeding (by 1.6 times) permissible safe levels (200 mg/kg FW). Treatments with B. subtilis or its combination with SA decreased Ph. infestans-activated tuber late blight incidence (by 30–40%) and reduced oxidative and osmotic damages (i.e., malondialdehyde and proline) and AMY activity in stored, infected tubers. Additionally, these treatments decreased pathogen-activated GA accumulation and increased ascorbic acid in stored tubers. Thus, the results indicated that endophytic bacteria B. subtilis, individually, and especially in combination with SA, have the potential to increase potato postharvest resistance to late blight and improve tuber quality in long-term storage.