Djokovic came out all guns blazing as he clinched the first set in just 26 minutes and dropped only 14 of 45 points in the process.
However, Darcis refused to go down without a fight as he took a 5-4 lead in the second.
But, that would be Darcis' only shining moment as Djokovic not only came back to level the set at 5-5, but surged ahead to take it and win the match in 88 minutes.
World number seven David Ferrer is also through to the fourth round after he defeated Lukas Rosol 6-4, 7-5.
Rosol will be left ruing his wastefulness in the opening set, with the Czech failing to convert multiple break points in the first and fifth games. He would pay the price, with Ferrer grabbing the first break of the match in the sixth game.
Having seen his opponent gain the advantage, Rosol at last broke Ferrer in the ninth game, but the Spaniard would break back to take the set.
Both players upped their game in the second set, with break points a rarity. Indeed, it was Ferrer who carved out the first break point in what would be the final game – and an epic one at that. In a game that included five deuces, Ferrer at last was able to convert his fifth match point.
In the day's final match, home favourite John Isner made surprisingly light work of ninth seed Grigor Dimitrov.
The 22nd-seeded Isner required just an hour and 17 minutes to beat the Bulgarian 7-6 (2), 6-2.
Earlier in the day, Japan's Kei Nishikori, who is ranked fifth, cruised past Viktor Troicki 6-2, 6-2 to reach the fourth round.
Joining him there is Canada's Milos Raonic, who beat Jeremy Chardy of France 6-1, 5-7, 7-6 (3) in a hard-fought contest that lasted two hours and 10 minutes.