Borders 8 (8)
Tries: De Luca.
Dragons 20 (10)
Tries: Black, Morgan.
Cons: Sweeney 2.
Pens: Sweeney 2.
Reivers were left to rue several missed opportunities as Newport-Gwent Dragons powered to a Magners League victory.
The visitors scored first in the 12th minute with a pick-and-drive sequence that ended with Adam Black going over.
Borders hit back with a Nick de Luca try before Ceri Sweeney, who had converted Black's score, exchanged penalties with Calum MacRae.
The Dragons sealed their second league win of the season thanks to another Sweeney penalty and a Kevin Morgan try.
Rain before kick-off made conditions treacherous and both sides found it difficult to string together decent passes in the early stages.
The home side were handed the first scoring opportunity with a penalty for handling in a ruck, but MacRae sent his 42-metre effort wide of the target.
Dragons made the most of the let-off with Black grabbing the game's first try, which Sweeney converted.
Reivers hit back when a kick from stand-off Steve Jones caused hesitation in the Dragons defence and De Luca pounced to score.
Sweeney kicked a three-pointer for the Dragons after Reivers were punished for killing the ball before MacRae replied with a penalty before half-time.
Referee Simon McDowell retired during the interval with a groin strain and was replaced by senior touch judge Andy Ireland.
Reivers could not convert their pressure into points.
MacRae was off the mark with his next penalty attempt while hooker Ross Ford spilled the ball close to the line when he looked likely to score.
A Sweeney penalty crashed against the upright and stayed out, but the player made amends when he converted Morgan's try before adding another penalty before the final whistle.
Reivers: Calum MacRae; Simon Danielli, Nick De Luca, Garry Law, Mark Robertson; Steve Jones, Brendan McKerchar; Gavin Kerr, Ross Ford, Bruce Douglas, Opeta Palepoi, Stuart Grimes (capt), Kelly Brown, Andy Miller, Ross Beattie.
Replacements: Sean Crombie, Ed Kalman, Craig Hamilton, John Dalziel, Rob Chrystie, Scott Gray, Gregor Townsend.
Dragons: Kevin Morgan (capt); Gareth Wyatt, Paul Emerick, Ashley Smith, Richard Fussell; Ceri Sweeney, Alex Walker; Adam Black, Ben Daly, Rhys Thomas, Ian Gough, Peter Sidoli, Joe Bearman, Jamie Ringer, Colin Charvis.
Replacements: Steve Jones, Lee Harrison, Luke Charteris, Nic Fitisemanu, Gareth Chapman, Mike Hercus, Gareth Baber.
Ref: Simon McDowell (Ireland).