Last season's runners-up Bordeaux have 38 points from 20 games, one behind Olympique Lyon, who had to be content with a 1-1 home draw with mid-table Lorient on Saturday.
"I'm really pleased with what I saw tonight", Bordeaux coach Laurent Blanc told reporters after his side thrilled the home fans with exciting moves.
"We had studied PSG's game well and we knew they would let us dictate play," the former France defender added. "We did that and certainly made the most of it."
France playmaker Gourcuff showed his class on 71 minutes, collecting the ball with his back to the goal just outside the box and setting himself up by rolling it back with the sole of his boot.
The gifted 22-year-old, already being compared with the great Zinedine Zidane, then turned around and twisted his way through two PSG defenders before hitting the back of the net with an angled shot to make it 3-0.
Gourcuff was later substituted to a standing ovation from the appreciative Bordeaux crowd and Brazilian substitute midfielder Fernando then wrapped up the win from close range.
Senegal defender Souylemane Diawara opened the scoring by heading home a Gourcuff free kick on 10 minutes and Argentine forward Fernando Cavenaghi made it 2-0 by tapping home a through ball by Mathieu Chalme 10 minutes from the break.
PSG, who had emerged as title contenders with wins over Lyon, Bordeaux and Olympique Marseille in the first half of the campaign, drop to sixth, six points off the pace.
"We had come here to pick at least one point and have to leave with none," PSG defender Sammy Traore told reporters. "This hurts but does not mean we're no longer ambitious. It just means we have a lot more work to do."
