The third-ranked Djokovic extended his Davis Cup winning streak to six singles.
Simon made Djokovic work for the victory, finally losing on a fourth match point after sending a backhand wide.
"You have to play each point and each match fully focused and the best you can," Djokovic. "I played great, although I had a little trouble in the end, which helped get him back into the game. The most important thing is that we won this point."
Simon, who dropped to 1-6 against Djokovic, said, "I knew I had to play my best tennis to defeat him, but unfortunately I didn't."
Tipsarevic double-faulted twice in losing the opening game in front of his hometown crowd in a sold-out Belgrade Arena and wasn't able to stay in rallies with the Frenchman.
"I think he was nervous today and did not play his usual way," Monfils said. "After the first set it was easier for me because Janko was under pressure."
The hero of the semifinal win over the Czech Republic recovered somewhat in the second set. But he failed to convert two break points at 1-1 and 3-3, and Monfils won the tiebreak.
"If I won that tiebreak, I think this would have been a different match for me," Tipsarevic said.
Another double fault by Tipsarevic gave the opening game of the third set to Monfils, who cruised to victory.
"The score looked easy, but it was tough," Monfils said. "I had to focus on all points."
Tipsarevic made 38 unforced errors to 14 by Monfils, who never lost serve.
France captain Guy Forget said his doubles team will remain as announced but suspected that Djokovic could replace Troicki.
"At 1-all, everything is open," Forget said. "That leaves the doubles very important. It could be crucial, and definitively we'll try to win."
The reverse singles Sunday are scheduled to start with Djokovic against Monfils, followed by Tipsarevic vs. Simon. France is seeking its 10th crown, the first since 2001.