Serbia, desperate to win a first title, were in cruise control before the veteran French pair battled back, chipping away at their rivals' confidence and the patience of a demanding home crowd to clinch a dramatic 4hr 33min battle at the Belgrade Arena.
"If they can win a match like that, they can win any match in the Davis Cup," said France captain Guy Forget.
Nine-time champions France had looked to be down and out when they were down 3-4, 15-40 in the fourth set, with Clement furious that a fan had shouted out while he was in his service action.
But he was inspired after that testing moment and the Serbian pair wilted, with their last opportunity coming when they had two break points in the eighth game of the decider that they were unable to convert.
The final will be decided in the singles on Sunday when Gael Monfils takes on world number three Novak Djokovic, while the final rubber is due to see Gilles Simon against Janko Tipsarevic.
Forget admitted that he may be tempted to use Llodra instead of Simon in what would be a decisive clash.
"I have some ideas. I want to speak to Michael later tonight, see how he feels, and speak with Gilles, because he's been going out there and playing with Gael," he said.
"We have one more point to win and two more matches to go. I'm going to try to put the best players possible. But Gael is ready for his first match against Novak."
Serbia coach Bogdan Obradovic said his team will bounce back on Sunday.
"I just want to congratulate my team. They play really great. They didn't have much luck, like the French team," he said.
"But still we are ready to fight tomorrow. We have two more matches, and we will give our best effort."
Clement and Llodra, who won the Wimbledon doubles title in 2007, started as slight favourites but they immediately had their backs to the wall on Saturday as Clement dropped serve in the fourth game, opening with a double fault and punching a volley long on break point.
Clement and Llodra had a point to break back at 3-5 down but a huge serve from Zimonjic pinned them back and two points later another big serve gave the Serbs the opening set 6-3.
The French picked up their game going into the second set but failed to convert two break points at 3-2 ahead on the Zimonjic serve before having to stave off two break points themselves five games later on Llodra's serve.
Serbia drew level at 5-5 and then profited from a sloppy service game from Clement, who gifted the break with a weak double fault.
Troicki served to put Serbia two sets up but failed to do so and there was uproar when he ran over to complain to the referee that a French fan had shouted during play in an effort to distract him.
That incensed the home crowd, who attempted to retaliate when Llodra was serving at the start of the tie-break.
Whether that worked or not was hard to tell, but the Serbs comfortably took the breaker 7-3 to go ahead two sets to love.
France bounced back in the third set thanks to a break in the second game as they launched their memorable comeback.