The young Pilgrims came from two goals down to claim the victory against a strong home team.
Argyle only got to Swindon 10 minutes before the scheduled 5.15pm start as they were held up twice through road traffic accidents. Not surprisingly they were slow to get going and found themselves 2-0 down inside the first 10 minutes.
But the Pilgrims responded well and reduced the arrears through Katie Grigg before Leah Johnson drew her side level.
Swindon regained the lead but back came Argyle, with Lilly Burton making it 3-3 at half-time.
The hosts scored again in the second half before Libby Lawton levelled again to set up a thrilling finish.
And it was Burton who snatched the winner as she got on the end of a strong run and cross from Lawton to get the young visitors off to a winning start.
The team had been entered in a new Devon under-18 league but this fell through so Argyle have to rely on friendly games. The good news is that teams such as Arsenal and Portsmouth and a number of other clubs have shown an interest in playing Argyle.
Argyle: Maisie Frickleton, Leah Johnson, Maddie Leopard, Chardonnay James, Beth Cowd, Esme Thompson, Milan Barros, Hollie Wade, Katie Grigg, Libby Lawton, Lilly Burton, Beth Riley.