The world number one, making his first appearance since winning the Australian Open, was tested early before claiming a 7-6 (7-5) 6-2 victory.
It marked Djokovic’s 50th career win at Indian Wells, where he is an equal-record five-time champion.
The Serbian will next face Philipp Kohlschreiber, the German having upset 31st seed Nick Kyrgios.
Djokovic fell behind an early break to Fratangelo, who consolidated for 4-2 but was unable to serve out the first set.
An outstanding break point saw Djokovic respond for 5-5 before Fratangelo grabbed the lead in the tie-break.
However, the American was unable to close it out, a double fault and a pair of errors handing Djokovic the opening set.
Djokovic broke in the first game of the second set and again in the fifth as he eased to victory.
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