Eight-time champion Rafael Nadal also had little trouble, beating Italian Andreas Seppi 6-1, 6-3, while fourth-seeded Roger Federer shook off a slow start in a 6-4, 6-1 win against Czech player Lukas Rosol.
The second-seeded Djokovic won his second-round opener in 45 minutes and has yet to be tested this week. He next faces Spaniard Guillermo Garcia-Lopez. The top-seeded Nadal has looked sloppy at times.
''Lost only two games in the first two matches (here). Can't be better than this, for sure,'' Djokovic said. ''I am confident on the court. I'm coming off a great American hard-court season.''
Djokovic sealed the 22-minute first set with a crisp forehand. Carreno Busta received loud cheers, clenched his fists and grinned broadly when he won his only game for 3-1 in the second. Djokovic served out, tormenting him one last time with an exquisite drop shot.
He is aiming for his fifth straight Masters win. He won at Indian Wells and Key Biscayne, dominating Nadal in the latter final to record his third straight win against him in straight sets.
''I've had more time comparing to last year to practice on the clay courts and to get my game to the level where I want it to be,'' Djokovic said.
Nadal achieved his 300th win on clay in beating Seppi. He won this title for eight straight years until last year when he lost the final to Djokovic.
''Today I played a little bit better than yesterday,'' Nadal said. ''I was playing at a good level.''
He next faces sixth-seeded David Ferrer, who easily beat Grigor Dimitrov of Bulgaria 6-4, 6-2, while Federer will face ninth-seeded Jo-Wilfried Tsonga.
Nadal has a 21-5 career record against countryman Ferrer, winning 10 of the past 11 meetings.
''David is a tough, tough player on any surface,'' Nadal said. ''But here on clay, always a big challenge.''
Rosol, meanwhile, broke Federer in the third game and held for 3-1.
''It was a bit rocky in the beginning,'' Federer said.
He broke back with a stinging cross-court forehand at Rosol's feet, and then broke him to love. He clinched the set when Rosol's forehand sailed long.
Federer has a 10-4 record against Tsonga, who beat him in the French Open quarterfinals last year and in the Wimbledon quarters in 2011.
''I've seen Jo play different kind of quality matches lately, so not quite sure he's going to play, how aggressive, how passive,'' Federer said.
Third-seeded Stanislas Wawrinka and eighth-seeded Milos Raonic of Canada also advanced for a quarterfinal matchup.
Having taken only 46 minutes to win his second-round match, Wawrinka didn't even need to lift a racket after Spaniard Nicolas Almagro pulled out because of pain in his left foot. Raonic beat Tommy Robredo of Spain 6-3, 6-4.
Tsonga won 5-7, 6-3, 6-0 against Fabio Fognini of Italy, who did his best to spoil the Frenchman's 29th birthday with his wild antics, including smashing rackets and shouting loudly.
In the day's only upset, Garcia-Lopez beat fifth-seeded Tomas Berdych of the Czech Republic 4-6, 6-3, 6-1.
The only other time Garcia-Lopez reached a Masters last eight was in Shanghai four years ago, when he lost to Djokovic, who leads 5-0 in their head-to-heads.