But Toulouse threatened a stunning comeback when Edwin Maka snatched a controversial try and matters were made worse when Daniel Leo was red-carded.
The hosts faced 15 minutes with just 14 men and five points between the sides. But they used every ounce of fighting spirit and character to hold the four-time Heineken Cup champions out and record a 30-19 victory.
"It's a very pleasing result in a big game," said Sid, who was named Amlin Man of the Match.
"We had some good periods and scored three tries but after that we gave away too many penalties and allowed Toulouse back into the game.
"It was very difficult after that but we refused to give up and the Catalan spirit helped us go on to win.
"The red card was really important but the way we scrummaged and defended on our try-line to keep Toulouse out, for me that was the reason why we won."
Perpignan were emotionally charged at Stade Aime Giral and a minute's applause was held for Samueli Naulu, who passed away following a car accident last week.
The wing made 12 European appearances for the Catalan giants and Sid dedicated the triumph to his former teammate.
"I salute Samu, a friend who has parted company prematurely. We will try to support his family and relatives. I just hope he was watching us from up there," said Sid.
Perpignanwill now face the winner of today's clash between Bath and Stade Francais, with the semi-finals to be held at the end of the month.
"We have a good history in the Heineken Cup and now the Amlin Challenge Cup. We are desperate to lift it," added Sid.
"I would prefer to face Bath as they are English and it is different. We play the French teams every year in the league. But it doesn't matter who we play as long as we win to reach the final."