The Serb, that now holds three of those four Grand Slam titles, has been beaten 6-4 6-4 by the German world number 3-9.
Djokovic struck his racquet in anger after Kohlschreiber – who had lost his past seven games against the 31-year-old – shot the first set.
Britain’s Kyle Edmund be at Radu Albot 6-3 6-3 to reach the final 16.
The game between Djokovic and Kohlschreiber began on Monday but was delayed until Tuesday because of heavy rain.
Kohlschreiber won 72% of first-serve points and saved four of five break points since he closed outside victory.
He will play French 18th seed Gael Monfils in the fourth round.
Nadala three-time champion at Indian Wells, did not face a rest point from the game.
He will play with Serbia’s Filip Krajinovic following Krajinovic, ranked 113, be at 15 th seed Daniil Medvedev 6-3 6-2.
Elsewhere, Canadian 19-year-old Denis Shapovalov rapped on court at his post-match interview later beating Croatian 10th seed seed Marin Cilic.
Hurzack, ranked 67 from the entire world, fought back to overcome Japanese lion seed Kei Nishikori 4-6 6-4 6-3.