New antibacterials are needed to tackle antibiotic-resistant bacteria. Type IIA topoisomerases (topo2As), the targets of fluoroquinolones, regulate DNA topology by creating transient double-strand DNA breaks. Here we report the first co-crystal structures of the antibacterial QPT-1 and the anticancer drug etoposide with Staphylococcus aureus DNA gyrase, showing binding at the same sites in the cleaved DNA as the fluoroquinolone moxifloxacin. Unlike moxifloxacin, QPT-1 and etoposide interact with conserved GyrB TOPRIM residues rationalizing why QPT-1 can overcome fluoroquinolone resistance. Our data show etoposide's antibacterial activity is due to DNA gyrase inhibition and suggests other anticancer agents act similarly. Analysis of multiple DNA gyrase co-crystal structures, including asymmetric cleavage complexes, led to a 'pair of swing-doors' hypothesis in which the movement of one DNA segment regulates cleavage and religation of the second DNA duplex. This mechanism can explain QPT-1's bacterial specificity. Structure-based strategies for developing topo2A antibacterials are suggested.