Global health is facing the immense threat of antibiotic resistance, and new therapeutic strategies are urgently needed. In the hospital setting, Acinetobacter baumannii is frequently responsible for multidrug-resistant (MDR), frequently-fatal infections. The use of phages, viruses that infect and kill bacteria, is an approach gaining considerable interest due to its versatility in treating MDR infections. Although phage therapy can quickly kill bacterial pathogens, resistance to phages arises rapidly. We isolated phages from sewage samples and demonstrated their lytic activity against two clinical strains of A. baumannii, AB900 and A9844. Co-incubation of the phages with their hosts resulted in the emergence of phage-resistant bacterial mutants, in which we identified the presence of remarkable fitness costs, including impaired growth, reduced production of capsule polysaccharides and decreased biofilm formation. As a result, phage-resistant isolates demonstrated a diminished capacity to colonise blood, liver, kidney and spleen within a BALB/c mouse model. Most importantly, we observed that phage-resistance was associated with a 2-fold reduction in the minimum inhibitory concentration (MIC) of the antibiotics ampicillin/sulbactam, ceftazidime and minocycline. Comparative bacterial genome analyses identified SNPs in genes coding for outer membrane proteins, suggesting their association with phage infectivity and fitness costs. We propose a practical therapeutic strategy whereby phages are firstly utilised to target MDR A. baumannii infections, followed by the predicted emergence of phage-resistant isolates exhibiting fitness costs that can be exploited using repotentiated antibiotics and the immune response. Our findings open the door for the clinical use of phage-antibiotic combinational therapy against MDR A. baumannii.