Neutrophils are major inflammatory cells that rapidly infiltrate wounds to provide antimicrobial functions. Within the damaged tissue, neutrophil migration behavior often switches from exploratory patrolling to coordinated swarming, giving rise to dense clusters that further disrupt tissue architecture. This aggregation response is self-organized by neutrophil paracrine chemoattractant signaling (most notably of the inflammatory mediator leukotriene B4 [LTB4]). The coordination mechanism and possible evolutionary benefits of neutrophil swarms are elusive. Here, we show that neutrophil swarms require mutual reinforcement of damage signaling at the wound core. New biosensors and live imaging in zebrafish revealed that neutrophil chemoattractant synthesis is triggered by a sustained calcium flux upon contact with necrotic tissue that requires sensing of the damage signal ATP. This "calcium alarm" signal rapidly propagates in the nascent neutrophil cluster in a contact-dependent manner via connexin-43 (Cx43) hemichannels, which are mediators of active ATP release. This enhances chemoattractant biosynthesis in the growing cluster, which is instrumental for coordinated motion and swarming. Inhibition of neutrophil Cx43 compromises clearance of wound-colonizing P. aeruginosa bacteria and exacerbates infection-induced morbidity. Thus, cooperative production of alarm signals among pioneer clustering neutrophils fuels the growth of dense antimicrobial cell masses that effectively seal off breached tissue barriers from opportunistic pathogens.