Defending champion Djokovic began his title defence with a straight-sets victory over Kazakhstani qualifier Andrey Golubev.
The top seed, winner of the event in 2008 and 2011, converted four of eight break points and rarely looked troubled en route to his 6-3 6-2 success in 80 minutes.
Despite advancing with ease, the Serbian was not totally satisfied and will look to move up a gear in round three when he takes on Kevin Anderson.
He said in a courtside interview: "We didn't play a beautiful match and there were a lot of unforced errors, but it's the opening match of the tournament for me and I am getting used to the conditions and the court.
"Hopefully the next match will be better."
South African Anderson progressed to a meeting with Djokovic when Germany's Philipp Kohlschreiber withdrew due to illness.
Home favourite Andy Roddick earlier advanced with a hard-fought three-set win over Poland's Lukasz Kubot.
Roddick lost the first set 6-4 but battled back to win the next in a tie-break and set up a decider.
He broke in the seventh game and clinched victory in Kubot's next service game, sealing a 4-6 7-6 (7/5) 6-3 win with his third match point.
He will face seventh seed Tomas Berdych after the Czech also came from a set behind to secure his last-32 place, despite serving eight double-faults and facing 15 aces from Sergiy Stakhovsky.
The Ukrainian took the first set on a tie-break but Berdych dug deep to win 6-7 (2/7) 6-3 6-4.
Roddick's big-serving compatriot John Isner (11) beat Frederico Gil 7-5 6-3, breaking the Portuguese lucky loser once in each set to progress.
Seeded Frenchmen Richard Gasquet and Julien Benneteau were knocked out, 16th seed Gasquet losing 3-6 7-5 6-1 to Spain's Albert Ramos while his 32nd-seeded compatriot lost 2-6 6-3 6-2 to Australian qualifier Matthew Ebden.
Other seeded players making early exits from the tournament included Kei Nishikori (17) and Florian Mayer (18), who lost in straight sets against Santiago Giraldo and Pablo Andujar respectively.
But eighth seed Mardy Fish made it through along with Nicolas Almagro (12), Gilles Simon (13), Juan Monaco (22) and Stanislas Wawrinka (23).