The three-time winner required a medical timeout in the final set, but he still had enough in the tank to claim a convincing 6-1 6-2 5-3 victory.
Prior to damaging his leg, Djokovic was soon into his rhythm as he twice broke his opponent's serve in the opening set, doing so in the second and sixth games.
Zeballos was again broken early in the second set and struggled to get a grip on the contest, finding himself 4-0 behind.
Djokovic saw things through and was once more in control of the third set, only to pull up with a muscular injury in the seventh game when 4-3 ahead.
The Serb found a couple of big serves to successfully hold once play had resumed, however, allaying any injury fears and setting up a meeting with either Bradley Klahn or Britain's Kyle Edmund in the next round.