World No. 1 and defending champion Novak round winners at the $4.695 million BNP Paribas Masters, the first ATP World Tour Masters event of the year.
Meanwhile, world No. 4 Andy Murray was upset in straight sets.
Djokovic handled qualifier Andrey Golubev 6-3, 6-2 in 80 minutes on the hardcourts at Indian Wells Tennis Garden.
The Serbian beat fellow two-time winner Rafael Nadal in last year's marquee Indian Wells finale. Djokovic also won this event in 2008.
He will face No. 29 seed Kevin Anderson in the third round. The South African moved on due to Philipp Kohlschreiber pulling out of their second-round match with an illness.
Murray fired four aces but lost to Guillermo Garcia-Lopez of Spain 6-4, 6-2. The fourth-seeded Brit forced seven break points against his opponent, but Lopez saves all of them.
American Andy Roddick, the 2009 Indian Wells finalist, outlasted Poland's Lukasz Kubot 4-6, 7-6 (7-5), 6-3.
Roddick will next do battle with seventh-seeded Czech Tomas Berdych, who beat Ukraine's Sergiy Stakhovsky 6-7 (2-7), 6-3, 6-4.
Americans John Isner, Mardy Fish and Ryan Harrison also posted wins on Saturday. Isner, the No. 11 seed defeated Portuguese lucky loser Frederico Gil 7-5, 6-3. The eighth-seeded Fish was leading Andreas Seppi 6-3, 3-2 when the Italian retired from the match, while Harrison discarded 25th-seeded Viktor Troicki 7-6 (7-5), 6-3.
Spainard Nicolas Almagro, the No. 12 seed, rallied to take down American Sam Querrey 5-7, 6-4, 6-4. Frenchman Gilles Simon, the 13th seed, beat Dudi Sela 7-5, 6-7 (6-8), 6-4.
Other second-round winners were Switzerland's Stanislas Wawrinka, Argentine Juan Monaco, Spain's Pablo Andujar and Albert Ramos, South African Matthew Ebden and Colombia's Santiago Giraldo.
The 2012 Indian Wells champion will collect $1 million.