The 25-year-old, who reached the second round at the Australian Open, had to work extremely hard to earn his spot in the second round in Pune.
The World No.1 impressively came from two sets down to beat the Italian on his way to securing a quarterfinal place.
The world number 1 was on the back foot in the opening two sets as the Italian teenager delivered a performance for the ages.
After winning his match in straight sets, the Serbian World No.1 will take on Federico Coria in the last eight.
On the back of the straight-set victories, Tsitsipas will play Lorenzo Musetti for a place in the final.
The massively talented 19-year-old Italian sensation Musetti has enjoyed a steady rise in international tennis till now