Man-of-the-match Jonny Wilkinson played a significant part in helping the visitors home, kicking 100 per cent and creating the only try of the night for Toby Flood as the northeasterners built on their 10-6 half-time lead.
After the bright sunshine of their first two days in the Limousin region, the grey clouds descended on Parc Municipal des Sports only an hour before kick-off, ensuring a rain-soaked and error-strewn 80 minutes of rugby.
The heavy surface dictated a low-paced start to proceedings, Brive nudging themselves ahead within three minutes as fly half Luciano Orquera slotted over a penalty from straight in front after chipping and chashing from half way.
Liberal interpretation from Italian referee Carlo Damasco led to a free-for-all at the breakdown throughout, while the Falcons' mauling game clicked in to gear with a string of gains in the driving phases as they forced three successive penalties in the Brive 22.
Home fullback Maxime Petitjean found the greasy underfoot conditions too much as he fell short with an ambitious 50-metre penalty attempt, and the hosts' cause was done no favours as centre Fabrice Estebanez was sin-binned for a late hit as Newcastle cleared their lines.
With tempers flaring on both sides another scuffle ensued only minutes later, but the first try finally came just after the half hour as Jonny Wilkinson chipped over the top of the flat defensive line and fellow England star Flood hacked on before diving on the loose ball to score.
Wilkinson had to wait for the thumbs-up from the video referee before adding the conversion which saw his side assume a 7-3 lead, but almost straightaway the advantage was reduced to a single point as Orquera's 40-metre penalty from the left hand side punished a reflex action high tackle from Kiwi flanker Brent Wilson.
A crunching hit from Ben Woods from a high ball afforded the Falcons a penalty on the 22 for not releasing the ball, which Wilkinson duly slotted through from right of the posts as he brought the first-half to a close with the visitors 10-6 to the good.
Straight from the restart the hosts tried to narrow the gap with an optimistic 45-metre drop goal attempt from Petitjean which never threatened the uprights, but with James Grindal sin-binned for slowing down a quick tap penalty in his own 22 Brive sensed a swing in momentum.
Orquera failed to take immediate advantage with a wayward kick from the resulting penalty on the left touchline, and the relieving boots of Flood and Wilkinson both averted danger from the visiting half in quick succession.
With Flood forced in to a makeshift scrum half role in Grindal's temporary absence, he found himself unusually steering the rolling maul from which Wilkinson stroked over his second penalty as Brive failed to cope with the driving power of the visitors.
Orquera negated that within three minutes as he clipped over a penalty from 40 metres out in front of the posts, but determined not to be outdone Wilkinson responded with an emphatic effort from the right touchline after sensational work at the tackle from Mathew Tait to force the penalty.
Brive's indiscipline was again to the fore as Fijian wing Norman Ligairi was sin-binned on the hour mark for launching an ill-advised flurry of punches on Wilson, but it was the hosts who made the next dent on the scoreboard as an Orquera penalty from 45 metres out in front sailed through the uprights to punish Newcastle for not releasing.
With the Falcons attempting to close down the final ten minutes Flood pinned back the Frenchmen in their own 22 with a deft tactical grubber, Newcastle going on to pinch the line out ball near the opposition try line as they applied pressure and ran down the clock in the same breath.
A feigned drop goal by Wilkinson almost put Tait in to space as the Falcons enjoyed territory and possession in the dying stages, utilising the pick-and-drive game to deprive Brive of the chance to go up the other end and score.
Man-of-the-match Wilkinson continued his 100 per cent strike rate with a sublime penalty from the left touch line to take the lead to seven points.
A nervous finale ensued as the video ref was asked whether or not Brive's rolling maul had rumbled its way over the visiting line, but with a heap of bodies and no clear evidence either way there was only ever one conclusion to reach, as the Falcons held on to claim a crucial European victory.
CA Brive Correze:
Pens: Orquera 4
Newcastle Falcons:
Tries: Flood
Cons: Wilkinson
Pens: Wilkinson 4
CA Brive Correze:
15 Maxime Petitjean
14 Ronnie Cooke
13 Suka Hufanga (Benjamin Dambielle, 68)
12 Fabrice Estebanez
11 Norman Ligairi (Nicolas Le Roux, 72)
10 Luciano Orquera
9 Jean-Baptiste Pejoine (captain, Gregory Mahe, 48)
1 Davit Kinchagishvili (Luke Harbut, 48)
2 Jean-Philippe Bonrepaux
3 Scott Franklin (Andres Bordoy, 56)
4 Fabien Domingo
5 Charl van Rensburg
6 Alex Manta (Vincent Forgues, 60)
7 Jerome Bonvoisin
8 Simon Azoulai (Ryno van der Merwe, 64)
Newcastle Falcons:
15 Tom May
14 Tim Visser
13 Mathew Tait
12 Toby Flood
11 John Rudd
10 Jonny Wilkinson
9 James Grindal (Lee Dickson, 68)
1 Joe McDonnell (Jon Golding, 50)
2 Andy Long (Matt Thompson, 50)
3 Carl Hayman
4 Andy Perry
5 Mark Sorenson
6 Brent Wilson
7 Ben Woods
8 Russell Winter (captain, Geoff Parling, 61)
Referee: Carlo Damasco (Italy)
Attendance: 8,224
