Djokovic, a wild-card entrant who is the event's top seed, got past Slovakia's Martin Klizan 6-3, 7-6 (4).
The Serbian star didn't serve effectively through most of the match, though Klizan's only two service breaks came in the second set. However, Djokovic had enough to get through the decisive tiebreaker.
Djokovic had been idle since falling in the second round of the Australian Open to Uzbekistan's Denis Istomin in a five-set thriller.
In other first-round matches Tuesday, second-seeded Rafael Nadal of Spain defeated Germany's Mischa Zverev 6-4, 6-3 in a battle of left-handers. The same pair met earlier this year in Brisbane, Australia, where Nadal also emerged with a win.
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Third-seeded Marin Cilic of Croatia needed three sets to get past Ukraine's Alexandr Dolgopolov 6-3, 4-6, 6-0. Fourth-seeded Dominic Thiem of Austria topped France's Gilles Simon 7-6 (7), 6-3.
Sixth-seeded Nick Kyrgios of Australia also advanced, rebounding to top Israel's Dudi Sela 3-6, 6-3, 6-3.
Jack Sock, fresh off winning the title in the Delray Beach Open, was bounced in the first round at Acapulco. Japan's Yoshihito Nishioka beat the American 3-6, 6-2, 6-1.
American Donald Young got a victory when Aussie Bernard Tomic was forced to retire due to the heat after Young won the opening set 7-6 (5). Tomic, however, was back in action Tuesday night for a doubles match, which he and partner Paolo Lorenzi of Italy lost 7-5, 6-2 to American John Isner and Spaniard Feliciano Lopez.
Another American, Sam Querrey, posted a 6-2, 4-6, 6-3 win over Great Britain's Kyle Edmund. Lorenzi won his singles match, eliminating Taiwan's Yen-Hsun Lu 4-6, 6-3, 6-4. Argentina's Juan Martin del Porto barely got past American qualifier Frances Tiafoe 6-4, 3-6, 7-6 (1).
In women's first-round action at Acapulco on Tuesday, only one seeded player fell. Croatia's Ajla Tomljanovic knocked off sixth-seeded Eugenie Bouchard of Canada 7-6 (4), 6-1. None of the other seeds in action dropped a set.
Top-seeded Mirjana Lucic-Baroni of Croatia defeated Switzerland's Belinda Bencic 7-5, 6-4. Third-seeded Jelena Ostapenko of Latvia beat Montenegro's Danka Kovinic 6-2, 6-2, and fourth-seeded Monica Puig of Puerto Rico got past Italy's Francesca Schiavone 6-4, 7-6 (4).
Fifth-seeded American Christina McHale beat French qualifier Fiona Ferro 6-4, 6-4.
Others to advance to the second round in the women's draw were Daniela Hantuchova of Slovakia, Germany's Julia Goerges and Americans Taylor Townsend and Madison Brengle.
