In contrast to RNA viruses, double-stranded DNA viruses have low mutation rates yet must still adapt rapidly in response to changing host defenses. To determine mechanisms of adaptation, we subjected the model poxvirus vaccinia to serial propagation in human cells, where its antihost factor K3L is maladapted against the antiviral protein kinase R (PKR). Viruses rapidly acquired higher fitness via recurrent K3L gene amplifications, incurring up to 7%–10% increases in genome size. These transient gene expansions were necessary and sufficient to counteract human PKR and facilitated the gain of an adaptive amino acid substitution in K3L that also defeats PKR. Subsequent reductions in gene amplifications offset the costs associated with larger genome size while retaining adaptive substitutions. Our discovery of viral “gene-accordions” explains how poxviruses can rapidly adapt to defeat different host defenses despite low mutation rates and reveals how classical Red Queen conflicts can progress through unrecognized intermediates. Display omitted Display omitted ► Poxviruses rapidly adapt against host defenses via highly specific gene amplification ► Gains in vaccinia fitness occur within only a few serial passages in human cells ► Gene expansions precede and can facilitate adaptation via point mutation ► Gene “accordions” reveal new mode of virus adaptation in double-stranded DNA viruses Despite low mutation rates, poxviruses evolve rapidly via gene amplifications, which facilitate the emergence of better-adapted versions of viral factors by increasing the sampling potential for mutations. Gene amplifications are only transient, revealing a gene “accordion” strategy for virus adaptation.