The astounding number of anti-phage defenses encoded by bacteria is countered by an elaborate set of phage counter-defenses, though their evolutionary origins are often unknown. Here, we report the discovery of an orphan antitoxin counter-defense element in T4-like phages that can overcome the bacterial toxin-antitoxin phage defense system, DarTG1. The DarT1 toxin, an ADP-ribosyltransferase, modifies phage DNA to prevent replication while its cognate antitoxin, DarG1, is a NADAR superfamily ADP-ribosylglycohydrolase that reverses these modifications in uninfected bacteria. We show that some phages carry an orphan DarG1-like NADAR domain protein, which we term anti-DarT factor NADAR (AdfN), that removes ADP-ribose modifications from phage DNA during infection thereby enabling replication in DarTG1-containing bacteria. We find divergent NADAR proteins in unrelated phages that likewise exhibit anti-DarTG1 activity, underscoring the importance of ADP-ribosylation in bacterial-phage interactions, and revealing the function of a substantial subset of the NADAR superfamily.