Entropic forces have been argued to allow bacteria to segregate their chromosomes during replication. In many bacterial species, however, specifically evolved mechanisms, such as loop-extruding SMC complexes and the ParABS origin segregation system, are required for chromosome segregation, suggesting that entropic forces alone may be insufficient. The interplay between and the relative contributions of these segregation mechanisms remain unclear. Here, we develop a biophysical model showing that purely entropic forces actually inhibit bacterial chromosome segregation until late replication stages. By contrast, we find that loop-extruders loaded at the origins of replication, as found in many bacterial species, alter the effective topology of the chromosome, thereby redirecting and enhancing entropic forces to enable accurate chromosome segregation concurrent with replication. In addition, our model indicates that locally acting origin separation mechanisms, such as the ParABS system, cannot redirect segregation-inhibiting entropic forces. We confirm our predictions with 3D simulations of a replicating polymer: purely entropic forces do not allow for concurrent replication and segregation; entropic forces steered by loop-extruders loaded at the origin lead to robust, global chromosome segregation; and origin separation alone is effective at early replication stages, but does not fully segregate terminal regions. Together, our results illustrate how entropic forces and loop-extrusion play synergistic roles during bacterial chromosome segregation, whereas locally acting mechanisms serve a complementary function.