Praggnanandhaa was playing with white pieces and his victory pushed home favourite Carlsen to the fifth spot in the points table.
Classical chess, also known as slow chess, allows players significant amount of time to make their moves, usually at least one hour.
Carlsen and Praggnanandhaa had drawn their previous three encounters in this format.
Praggnandhaa’s sister R Vaishali held the top spot in the women’s competition, also with 5.5 points.
She drew her game against Anna Muzychuk. In other games, world number two Fabiano Caruana of the USA defeated reigning world champion Ding Liren of China. Liren dropped to the bottom of the heap in the six-player field following the loss. American Hikaru Nakamura won his Armageddon game against Alireza Firouzja of France to earn an extra half point and be third in the standings.
Nakamura will be up against Praggnanandhaa in the fourth round.