The goalkicking half-back had been on a drip in the build-up to the game in Perpignan after contracting a virus but he was the architect behind a five-try victory that keeps the Giants just a point behind Super League leaders Wigan.
"It rates as a very, very dogged and determined win," said Huddersfield coach Paul Anderson. "Broughy's been on a drip for a few days. He's not been well. He got a virus. His wife was sick at the airport and his kids have been ill as well."
He added: "We had a lot of adversity. A lot of barriers kept being put in front of us but we kept knocking them down. The commitment and camaraderie amongst the group were clear to see."
Huddersfield also overcame the 54th-minute dismissal of scrum-half Luke Robinson, who was sent off by referee James Child for making contact with full-back Morgan Escare's head in an off-the-ball tackle.
Centre Joe Wardle scored two tries, one of them from a spectacular 80-metre move sparked by a touch of brilliance from Brough, and hooker Shaun Lunt put the finishing touches to a fifth successive win with his 13th try of the season a minute from the end.
The visitors were trailing 16-14 at the time of Robinson's dismissal but rallied magnificently to produce a rousing finale and extend their winning run to five matches.
Wary of a clampdown on Super League coaches criticising referees, Anderson was tight-lipped over the sending-off but admitted the incident re-energised his team.
"I am very angry but I like my money," he said. "I'm not allowed to say the truth.
"I don't know why it is but history shows that it does galvanise a team. Perhaps it focuses your attention a bit more. You are down a man so you have to work even harder."