Abstract Non-enzymatic RNA self-replication is integral to the ‘RNA World’ hypothesis. Despite considerable progress in non-enzymatic template copying, true replication remains challenging due to the difficulty of separating the strands of the product duplex. Here, we report a prebiotically plausible solution to this problem in which short ‘invader’ oligonucleotides unwind an RNA duplex through a toehold/branch migration mechanism, allowing non-enzymatic primer extension on a template that was previously occupied by its complementary strand. Kinetic studies of single-step reactions suggest that following invader binding, branch migration results in a 2:3 partition of the template between open and closed states. Finally, we demonstrate continued primer extension with strand displacement by employing activated 3′-aminonucleotides, a more reactive proxy for ribonucleotides. Our study suggests that complete cycles of non-enzymatic replication of the primordial genetic material may have been catalyzed by short RNA oligonucleotides.