Skipper Colin Charvis led the way with two second-half touchdowns and Jamie Noon, Matt Burke and Tom May notched the others.
Brive were 22 points adrift at the break and all at sea by the end.
In the other game in Pool Four, Border Reivers had to dig deep to avoid embarrassment in Italy where L'Aquila were full value for their 22-12 half-time lead.
Tries by Uruguay international Andrea Brignoni launched the home offensive and by the break scrum-half Juan Cruz Legora and wing Roberto Mariani had followed suit.
The Reivers responded with two tries of their own before they found their form after the break to run out 32-25 victors, with five tries in total.
Charles Hore contributed 17 points, including two tries, while full-back Stuart Moffatt also scored a double to secure a bonus point.
The other Reivers try came from Scottish wing Simon Danielli.
Pat Sanderson got his quest for a third European Challenge Cup winners' medal off to a flying start as he bagged one of Worcester's five tries in their 36-18 home win in Pool Five over Montpellier.
A winner with NEC Harlequins in 2001 and 2004, the Warriors skipper was the guiding light as the English side kept their noses in front in the first half before stretching away after the break to extend their lead and pick up a bonus point.
New recruit Shane Drahm got the first of Worcester's five tries and he ended the game with a 16-point haul as he knocked over four conversions and a penalty.
Sanderson's score, and a penalty try, gave Worcester a 22-15 lead before teenage wing Uche Oduoza and former England scrum-half Andy Gomarsall wrapped up proceedings in the second half.
Montpellier, who won the European Shield in 2004, crossed the home line twice in the first half, but could only manage a penalty after the break.
Not to be outdone, Connacht ran in 10 tries in their 62-17 demolition of Amatori Catania in Galway. Keith Matthews led the way with a hat-trick and there were two each for Darren Yapp and Conor McPhillips.
The home side were completely in control from first to last and were 31-12 ahead at the interval.
Another 31 points followed in the second half with Paul Warwick, Matt Mostyn and Colm Rigney also among the try scorers.
It did not take long for former All Black flanker Sam Harding to find his feet in Europe as he crashed over for the first of Northampton Saints' seven tries in their 47-25 Pool One victory over Viadana at Franklins Gardens.
Harding got on the score sheet after only five minutes and his lead was followed by wings Ben Cohen and John Rudd.
Cohen scored a hat-trick and Rudd got two. Jon Clarke got the other try and skipper Bruce Reihana kicked 12 points.
In Pool Two, Agen were far to powerful for Rugby Parma, running in seven tries in their 50-23 away win, while there was a scare for Toulon in Romania in Pool Three as Bucuresti stole a point and almost a whole lot more as they were eventually beaten 20-16 by their French visitors.