It was a slow start with the first score not coming until after 30 minutes with a try from Brive hooker Thomas Acquier. The visitors' full back Romain Sola missed the conversion attempt to add to his two earlier penalty attempts kicked wide.
Five minutes later, Academy back Rory Parata crossed for the home side’s first try and his second in seven days. Outhalf Jack Carty, who had kicked an earlier penalty, sent the difficult conversion attempt wide.
The Athlone man made up for it just before the break, with a successful kick at the posts.
Half time: Connacht 11 – 5 Brive
Pat Lam’s men started the second half strongly, with a well worked team move that saw second row Ben Marshall, on his return from injury, cross in the corner in his first start for the province.
The celebrations were short lived as Brive responded immediately with a five-pointer from their winger Benito Masilevu after an impressive break from the visitors.
The French side made four substitutions just before Ireland international Kieran Marmion crashed over for his side’s third try in the corner.
With three tries in the bag, Connacht went in search of the bonus point but a series of injuries that saw two front rowers pack down in the back row towards the end of the game, made the task all the more arduous.
It was a nervy finish for all at the Sportsground as Brive forced their way back into the game with a 73rd minute try from replacement back Sevanaia Galala, converted by scrum half Teddy Iribaren.
Leading by just four points, Connacht were forced to defend in the dying minutes of the game but got the crucial turnover in their own 22 as the clock hit 80.
Full time: Connacht 21 – 17
Referee: Craig Maxwell-Keys
Man of the Match: Niyi Adeolokun