The world number two and four were in charge from the start and bossed the rubber from the net and the baseline to win 6-3, 7-5, 6-4.
The win means that the Swiss are just one victory away from capturing the first Davis Cup title in their history.
That could come Sunday when the reverse singles are held, with Wawrinka and Federer highly likely to play again against Gael Monfils and Jo-Wilfried Tsonga.
“Clearly it’s a big relief. The medical staff, it’s a big thanks to them. Thanks for getting me back onto the court. Stan has been unbelievably supportive,” said Federer, who had been struggling with a back injury in the days prior to Lille.
“I am really happy with the way we were playing today. We were really aggressive, we knew what we had to do. I think we did a good job,” said Wawrinka.
Watched by another huge crowd of around 27,000 in the roofed over Lille football stadium, including French President Francois Hollande, the Swiss pair knuckled down quickly to their task, pocketing the first break of the match in the sixth game on the Benneteau serve.
That was enough to edge them a set up, but, after a quick visit to the locker room to regroup, the French pair came back out re-energised.
They briefly looked the likelier to move back into contention, but failed to convert any of five break points that came their way in the second, fourth and eighth games.
They were made to pay a heavy price as, with a tie-break looming, Gasquet’s serve collapsed under the weight of some magnificent returns from both of the Swiss.
A Federer backhand winner secured the break and Wawrinka had no trouble serving out for a two sets to love lead.
The French pair had a mountain to climb and they had to hold on grimly to Gasquet’s serve early in the third set to stay in the match.
Two games later it was Benneteau’s turn to feel the Swiss pressure and, after the French pair saved two break points, they succumbed on the third, Wawrinka splitting them with a forehand drive.
The Swiss were coasting towards a famous victory and, even though the home pair saved a match point on Benneteau’s serve at 3-5 down, Federer made no mistake in serving to love for the match and what could turn out to be the pivotal point of the final.
In Friday’s opening singles, Wawrinka defeated Tsonga in four sets and Monfils stunned Federer in three.
After his defeat, Federer insisted that his injured back was on the mend and that he would be fit for action at the weekend.
He and Wawrinka won Olympic doubles gold in Beijing for Switzerland in 2008, but they had lost the last four Davis Cup doubles they had played together.
By putting an end to that dire run of defeats they have put their country on the brink of one of its greatest ever sporting achievements.
It would also be a consecration for Federer, who has won an all-time best of 17 Grand Slam titles, but, unlike his great rival Rafael Nadal, he has yet to win the Davis Cup.
The signals are all at green for the Swiss as six out of seven teams which have won the doubles when Saturday started at 1-1 have gone on to capture the Davis Cup.
French skipper Arnaud Clement though knows that France still have a shot at a first Davis Cup win since 2001 with Monfils in superb form and Tsonga having defeated Federer the last time they played in Canada in August.