The top-seeded Serbian, who has claimed four of the last five Grand Slam titles, took some time to settle in to his first career meeting with Carballes Baena but after a tight first set was off to the races.
Djokovic got an early break to go ahead 2-0 in the second set and never looked back as the three-times champion used a mix of deft volleys, solid movement and great instincts to remain undefeated in 14 career first-round matches in New York.
Carballes Baena looked up for the task early on as he fought off a trio of break points to hold for 1-1 in a game that lasted nearly 10 minutes.
The Spanish world number 76 kept up the fight and was serving at 4-5 in the opening set but Djokovic sent a backhand volley to an empty court to set up a pair of break points and converted on his first chance.
Djokovic was never tested the rest of the way and did not face a break point in the entire match.
Up next for Djokovic will be either American Sam Querrey or Argentine Juan Ignacio Londero.
Earlier, Kei Nishikori became the first man to advance to the US Open second round as the 2014 finalist beat qualifier Marco Trungelliti, who was forced to retire with the Japanese leading 6-1 4-1.
Reilly Opelka scored the biggest upset of the US Open so far on Monday, defeating 11th seed Fabio Fognini 6-3 6-4 6-7(6) 6-3 to win his first main-draw match at the tournament.
World No.5 Daniil Medvedev continued his recent good form with a 6-4 6-1 6-2 first-round win over Prajnesh Gunneswaran of India, despite taking a medical timeout for treatment.
On the women’s side, French Open champion Ashleigh Barty survived a first-round scare, staving off 25-year-old Zarina Diyas 1-6 6-3 6-2 after struggling to find her footing as the action kicked off at Arthur Ashe Stadium.
Venus Williams ended a run of suffering first-round exits at Grand Slam tournaments by walloping China's Zheng Saisai 6-1 6-0, while Latvian 12th seed Anastasija Sevastova dispatched an error-prone Genie Bouchard 6-3 6-3 to reach the second round.
Kristina Mladenovic upset former world number one Angelique Kerber 7-5 0-6 6-4 on Monday to put an early end to the 2016 US Open champion's bid for a second trophy at Flushing Meadows.