The Irish side used the strong winds at their backs to good advantage with full-back Darragh Leader and Ireland centre Bundee Aki both crossing for tries, converted by Australian fly-half David Horwitz.
In atrocious conditions play became scrappy but a Horwitz penalty extended Connacht’s advantage before Perpignan replacement hooker Manu Leiataua crossed for a try and full-back Jonathan Bousquet converted to add to an earlier penalty.
Leiataua turned villain as he was sin-binned with ten minutes remaining for dissent and Perpignan lost all momentum as a result.
Helped by the extra man advantage, Connacht secured the victory when Australian centre Kyle Godwin touched down three minutes from time.
Perpignan, who have just two points from their first three games in the competition, will try to gain revenge with they play hosts to Connacht in France on Friday evening.