CRISPR loci are a cluster of repeats separated by short "spacer" sequences derived from prokaryotic viruses and plasmids that determine the targets of the host's CRISPR-Cas immune response against its invaders. For type I and II CRISPR-Cas systems, single-nucleotide mutations in the seed or protospacer adjacent motif (PAM) of the target sequence cause immune failure and allow viral escape. This is overcome by the acquisition of multiple spacers that target the same invader. Here we show that targeting by the Staphylococcus epidermidis type III-A CRISPR-Cas system does not require PAM or seed sequences, and thus prevents viral escape via single-nucleotide substitutions. Instead, viral escapers can only arise through complete target deletion. Our work shows that, as opposed to type I and II systems, the relaxed specificity of type III CRISPR-Cas targeting provides robust immune responses that can lead to viral extinction with a single spacer targeting an essential phage sequence.