After thumping Zebre in their opener, Connacht made the perfect start in their bid to make it two victories from as many matches in Europe as Ralston sniped in from close range after seven minutes.
Jack Carty converted to give the visitors the perfect start at the Stade Aime Giral.
Things got even better four minutes later when De Buitlear crossed after a maul, and Carty again added the extras.
Prop Boyer-Gallardo got Perpignan on the board in the 17th minute, and Aucagne’s penalty nudged the hosts to within six points.
However, Connacht ended the half on top and wing Mullins darted over in the 37th minute for give Pete Wilkins’ side a 19-8 half-time advantage.
That lead was almost wiped out by a flurry of Perpignan points in the opening 10 minutes after the restart. Aucagne kicked a penalty before wing Joseph crossed out wide.
Fly-half Aucagne then converted to bring the French side to within one point.
However, Connacht weathered the storm and managed to see out the game.
Replacement back row Boyle put daylight between the sides with the bonus-point score, and better was to come when former Ulster hooker Adam McBurney crossed late on.
Perpignan: Crossdale; Joseph; Buliruarua, Naqalevu; Granell; Aucagne, Hall; Boyer-Gallardo, Lam, Roelofse; Ortombina, Warion; Schiava, Hicks, Dvali.
Replacements: Montgaillard, Barcenilla D’Onghia, Brookes, Chinarro, Fa’aso’o, Aprasidze, Allan, Duguivalu.
Connacht: Cordero; Mullins; Ralston, Forde; Smith; Carty, Devine; Buckley, de Buitlear, Illo; Murray, Joyce; Prendergast, Hurley-Langton, O’Brien.
Replacements: McBurney, Duggan, Aungier, Dowling, Boyle, Murphy, Hawkshaw, Oliver.
