Phages are promising tools to fight antibiotic-resistant bacteria, and as for now, phage therapy is essentially performed in combination with antibiotics. Interestingly, combined treatments including phages and a wide range of antibiotics lead to an increased bacterial killing, a phenomenon called phage-antibiotic synergy (PAS), suggesting that antibiotic-induced changes in bacterial physiology alter the dynamics of phage propagation. Using single-phage and single-cell techniques, each step of the lytic cycle of phage HK620 was studied in E. coli cultures treated with either ceftazidime, cephalexin or ciprofloxacin, three filamentation-inducing antibiotics. In the presence of sublethal doses of antibiotics, multiple stress tolerance and DNA repair pathways are triggered following activation of the SOS response. One of the most notable effects is the inhibition of bacterial division. As a result, a significant fraction of cells forms filaments that stop dividing but have higher rates of mutagenesis. Antibiotic-induced filaments become easy targets for phages due to their enlarged surface areas, as demonstrated by fluorescence microscopy and flow cytometry techniques. Adsorption, infection and lysis occur more often in filamentous cells compared to regular-sized bacteria. In addition, the reduction in bacterial numbers caused by impaired cell division may account for the faster elimination of bacteria during PAS. We developed a mathematical model to capture the interaction between sublethal doses of antibiotics and exposition to phages. This model shows that the induction of filamentation by sublethal doses of antibiotics can amplify the replication of phages and therefore yield PAS. We also use this model to study the consequences of PAS on the emergence of antibiotic resistance. A significant percentage of hyper-mutagenic filamentous bacteria are effectively killed by phages due to their increased susceptibility to infection. As a result, the addition of even a very low number of bacteriophages produced a strong reduction of the mutagenesis rate of the entire bacterial population. We confirm this prediction experimentally using reporters for bacterial DNA repair. Our work highlights the multiple benefits associated with the combination of sublethal doses of antibiotics with bacteriophages.