The 16-year-old, originally from Bristol, became Great Britain’s youngest ever Fed Cup player after Judy Murray gave her the nod following Johanna Konta’s withdrawl through injury.
The British number ten fully justified her captain’s decision with a relatively comprehensive 6-3 6-3 over her Georgian opponent.
Heather Watson then beat Sofia Shapatava 6-2 6-0 to see Britain top their pool.
Swan will now be part of the team that faces either Belgium or Bulgaria in Saturday’s play-off.
