Djokovic was broken early in the deciding set, but he broke back in the sixth game and then closed out the match with another break in the final game.
"I feel a bit lucky, but I think you have to work for luck," Djokovic said. "It doesn't just fall through the sky. I think I fought my way through in the match, really believed until the end, and mentally, this is a very important win for me."
Djokovic won the Australian Open in 2008, and added the Masters Cup title at the end of last season. At this year's Australian Open, he retired against Andy Roddick in the quarterfinals.
"If I want to stay on top of the men's game, I have to win these matches," Djokovic said.
Simon rued his missed opportunity.
"I think I had enough chances to win this match, but finally I lost it," the Frenchman said. "That's why it is a very bad match for me."
Ferrer looked good throughout his win over Gasquet.
"This was the best match of the season for me," the 26-year-old Spaniard said. "I was very consistent and very focused. But even though the score reads 6-2, 6-2, it was a tough match and I think I was a bit lucky as well, because I saved a few break points during the match."
From his side of the court, Gasquet could do little.
"He played really well. That's the worst guy for me to play against," Gasquet said. "His game is the worst for me because he has no faults in his game he has a big backhand, big forehand and he runs everywhere, so that's really hard for me."