French hopes of a 10th crown now rest with Michael Llodra, who will line up against Viktor Troicki in the fifth and final rubber.
Serbia were left on the ropes after Llodra and Arnaud Clement handed France a stunning comeback victory in the doubles on Saturday after being led two sets to nil.
However, Djokovic helped redress the balance with a commanding display of tennis which seemed to leave Monfils, who won his opening rubber Friday against Tipsarevic, frozen out of the game.
"It's one of the best matches of my career, in the circumstances," said Djokovic. "I have a lot of respect for the French team, especially Gael, who is a good friend. Now, I'm hoping Serbia can go on and take the victory."
Djokovic set the bar high from the outset with a service game which had the Frenchman struggling and gave the world number three his first 14 points of the match.
In the first set, Djokovic broke Monfils twice as he surged to a quick 6-2 win.
Monfils was soon in panic mode, and seemed only a pale shadow of the player who swept Tipsarevic aside on Friday.
The Frenchman battled back bravely in the second set, trying on several occasions to upset his opponent's plans with brief forays to the net.
But while that strategy worked on occasion, Djokovic somehow managed to restore his preferred strategy of unleashing thunderous shots from the baseline, a game in which he was ultimately superior.
The Serb broke Monfils again in the sixth game of the second set, and then in the final game, spreading his arms in mock triumph towards the increasingly vociferous partisan crowd as he surged to a 2-0 lead.
To his credit, Monfils upped his game in the third set, the world number 12 breaking Djokovic twice -- only to cancel that advantage by losing his own service game due to a series of unforced errors.
Djokovic eventually secured the win to register his sixth defeat of Monfils in as many meetings.
"I'm very disappointed, I expected to play a lot better," Monfils told France 3 television. I gave it everything I had. After talking to Guy (Forget, team captain) I tried to change tactics a few times because Novak was so strong. He was by far the better player today."
He added: "Mika (Llodra), is feeling great. He's recovered well (from Saturday's doubles) and he's used to playing in singles.
"I know he will give it everything he has."