The South American advanced to the third round with a 2-6, 6-4, 6-4 win against the 24-time Grand Slam champion, who hit the wall in the second set but recovered to make a battle of it in the third before bowing out.
The Serb star won a brutal 18-minute third game of the second set after taking the first, saving four break points over nine deuces.
But he was clearly struggling, doubling over or even dropping to his hands and knees between some points.
Djokovic took a medical timeout after that game, with the physio and then a doctor coming on court to assist with assessments and ice towels.
After Tirante took the second set, both players cooled off in the locker room.
Slightly revived, Djokovic soldiered on in the deciding set, where a drop shot gone wrong on his opponent's match point spelt the end for the veteran - who must try to regroup before the start of the US Open on August 30th.