Competition in animals involves a wide variety of aggressive behaviors. One of the most sophisticated strategies for a focal actor is to provoke a competitor into uncontrolled aggression toward other competitors. Like animals, bacteria rely on a broad spectrum of molecular weapons, some of which provoke potential rivals by triggering retaliation. While bacterial provocation is well documented, its potential adaptive value has received little attention. Here, we examine the costs and benefits of provocation using mathematical modeling and experiments with <i>Escherichia coli</i> strains encoding colicin toxins. We show that provocation is typically costly in one-to-one encounters because a provoking strain receives a strong reciprocal attack compared with nonprovoking strains. By contrast, provocation can be strongly beneficial in communities including more than two toxin-producing strains, especially when the provoker is shielded from, or resistant to, its opponents' toxins. In these scenarios, we demonstrate that the benefit of provocation derives from a "divide-and-conquer" effect by which aggression-provoking toxin producers force their competitors into increased reciprocal aggression, leading to their cross-elimination. Furthermore, we show that this effect can be mimicked by using antibiotics that promote warfare among strains in a bacterial community, highlighting the potential of provocation as an antimicrobial approach.