The visitors scored an early try by Tom Sparshott to lead 5-0 at half time but the Exiles dominated the second half and equalised with a well worked try with fifteen minutes to go through Jack Harrison.
The Dragons defended well and with time running out broke from their own 22 and were awarded a penalty which Ted Senior converted from in front of the posts to take what proved to be a winning lead. The Exiles finished strongly but the visitors held out.
Exiles Squad Manager Gareth Davies said afterwards: "The Dragons are a very well organised side and were difficult to break down. We are pleased with our performance but unfortunately we couldn't convert our territory into points.
"That said, in the circumstances, our players were outstanding and will certainly learn from this experience".
Exiles Secretary Terwyn Williams added: "Considering our players only got together a couple of hours before kick off I thought we did extremely well. The commitment and enthusiasm of the boys was outstanding and they were all a real credit to the Exiles."
Richard Bayliss, Ivybridge College, Devon; Tom Mumford, Ivybridge College, Devon; Ben Edwards, St. Peter's, Surrey; Jordan Cox, Stanbridge, Hampshire; Rhys Verley, Queensmead, Middlesex; Ryan Brett-Williams, Bedford School, East Midlands; Tom Poynder, Worth School, Sussex; Tim Whitefield, Woodlands Academy, Coventry; Kiran Preddy, St. Olave's, Kent; Andrew Oxley, Gateshead College, Tyne and Wear; Joel Parsons, Hartpury College, Gloucestershire ; Robert Stevenson, Sedbergh School, Cumbria; Rhys Hughes, North Bristol Centre; Luc Jones, Woking College, Surrey; Jack Harrison, Ardingly School, Sussex; Dexter John, Kettering, Northants; Callum Lambotte, Oakwood Park, Kent; Will Pinnell, Hartpury College, Gloucestershire; Ash Armel-Close, Isleworth and Syon, Middx; Celyn Beynon, Queen Elizabeth's School, Dorset; Will van Klaveren, Kings College School, Wimbledon.