Djokovic, the world number two, is the highest ranked player remaining at the Masters event in Indian Wells after Rafael Nadal's exit on Monday, although the Serb was pushed all the way by Gonzalez on Tuesday before prevailing 6-1 3-6 6-1.
It took Djokovic one hour and 37 minutes to move into the last-16 of the hard-court tournament, finally seeing off the 91st-ranked Gonzalez.
Djokovic will need to be on his game if he is to make the quarter-finals, with comeback king Marin Cilic his next opponent.
Cilic, the 24th seed from Croatia, beat Spanish 12th seed Tommy Robredo 6-4 6-3 to continue his stellar start to 2014.
After serving a nine-month ban for a doping violation, Cilic has returned to the tour with aplomb - claiming titles in Zagreb and Delray Beach, and his triumph over Robredo meant he was the first ATP Tour player to notch 20 match wins in the calendar year.
The only remaining top-20 player in Djokovic's half of the draw is American John Isner, after Richard Gasquet and Grigor Dimitrov were third-round casualties.
Gasquet, the eighth seed of France, fell to Spanish 30th seed Fernando Verdasco 7-6 (7-5) 6-1, while Bulgarian Dimitrov - the 15th seed - coughed up a lead to go down to Latvia's Ernests Gulbis 2-6 6-1 7-5.
Gulbis, the 20th seed, turned the tables on Dimitrov from their clash in the Abierto Mexicano quarter-finals recently, and his run in California follows his good form in winning the Marseille title in February.
Verdasco will face the 12th-seeded Isner in the fourth round, after the latter dispatched of Taipei's Yen-Hsun Lu 6-4 6-3.
Awaiting Gulbis next is Spain's Roberto Bautista-Agut, who saw off the valiant challenge of Finland's Jarkko Nieminen 6-2 4-6 7-6 (8-6).
Spain's Feliciano Lopez continued to capitalise on his open draw, as he fought back to beat Kazakhstan's Mikhail Kukushkin 1-6 6-3 6-4 to move into the fourth round.
Lopez has benefitted from the withdrawal of sixth seed Juan Martin del Potro earlier in the event, and the left-hander will face France's Julien Benneteau next.
Benneteau ended the dream run of Austrian qualifier Dominic Thiem 7-6 (7-4) 6-3.
Djokovic grinds out win at Indian Wells
