Brive had their own star in centre Suka Hufanga who scored two tries and gave the scoring pass for their third.
The Dragons started strongly with Captain Morgan leading from the front as he grabbed an early brace of tries. It took just five minutes for the first, despite the Dragons playing against a strong wind in the first period. The home side launched a series of attacks with the back row of Michael Owen, Colin Charvis and Jamie Ringer prominent, with Morgan on hand to finish off from close range.
He had rather further to go for his second try, a forty yard run from turnover ball which left the defence flat-footed. Ceri Sweeney missed both conversions and Brive took that opportunity to come back strongly.
Centre Suka Hufanga was denied by a forward pass when wing Alexis Palisson had been a better option, but Hufanga was soon to turn provider. The visiting back row made the break up the middle and the centre was on hand to give right wing Filimone Boleavucu the scoring pass. Luciano Orquera converted from the right hand touchline to narrow the margin to 10-7.
However, the Dragons hit back strongly, first when they decided to go for the corner with a kickable penalty. It proved to be the right decision as Ringer gave the scoring pass to prop Adam Black.
Then, as half-time approached, more turnover ball allowed the Dragons to work wing Gareth Wyatt free. He sprinted fifty yards with lock Peter Sidoli in support; when he was illegally prevented from passing a penalty try was awarded by referee Wayne Barnes. Sweeney converted both to make it 24-7 at half-time.
Brive would not have held out much hope for the second half, well behind, up against a strong wind and just to make life more miserable a driving rain which started during the interval.
Matters were made even worse when they could not control a line-out on their own line and Ringer pounced to grab the try. Sweeney converted from touch.
That sparked Brive's best attacking period: a series of line-outs on the Dragons line and a try-scoring chance from a break by Boleavucu, but his pass to Hufanga was put down.
However, more pressure brought the sin-binning of Charvis for a professional foul as the substitutions began to flow from both sides. Brive were able to close the gap and again Hufanga was the key man, catching scrum half Tim Clark's chip ahead from turnover ball. Hufanga went 40 yards to the corner with a clear run because the Dragons had been lined up to attack the other side of the pitch.
Another Brive attack, another Clark chip and another Hufanga try, under more pressure this time, closed the gap to 31-17. That roused the Dragons and they reopened the margin to more than two scores with a Sweeney penalty from under the Brive posts.
Wing Aled Brew put the icing on the cake with a well taken try after a series of attacks left him a clear run to the line.
Dragons 39-17 Brive
Dragons: Tries: Morgan 2, Black, Penalty try, Ringer, A Brew. Cons: Sweeney (3). Pens: Sweeney
Brive: Tries: Boleavucu, Hufanga (2). Cons: Orquera
Dragons: K Morgan (Capt); G Wyatt, P Emerick, N Brew, A Brew; C Sweeney, A Walker; A Black, B Daly, L Harrison, I Gough, P Sidoli, C Charvis, J Ringer, M Owen
Replacements: S Jones, J Corsi, D Maddocks, L Charteris, N Fitsemanu, G Cooper, A Thomas
Brive: N Le Roux; F Boleavucu, L Valbon, S Hufanga, A Palisson; L Orquera, T Clark; P Lafond, J Djoudi, P Capdevielle, C Petre, C van Rensburg, S Azoulai (capt), A Maleyrie, D Chouly
Replacements: J Campo, P Toderasc, F Domingo, J Bonvoisin, J Pejoine, M Petitjean, S Bonetti