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, bidding for a 17th grand slam title, 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 secure the win.
Up next for Djokovic will be either American Sam Querrey or Argentine Juan Ignacio Londero.