The Serbian broke his racket in anger after dropping the first set to Kohlschreiber.
Kohlschreiber posted his first victory over a top-ranked player, advancing to a fourth-round where he will face France's Gael Monfils.
Djokovic, playing his first tournament since lifting his record seventh Australian Open title in January, knew he'd have to work his way back into top form.
"It's a very special win today", Kohlschreiber said after the match.
Two wayward forehands and a double fault from Djokovic helped Kohlschreiber to another break for a 5-2 lead.
Novak Djokovic had no answer
Her win over Halep, a former world No. 1 and victor at Indian Wells in 2015, comes after she dispatched 2018 finalist Daria Kasatkina in the second round and former French Open champion Jelena Ostapenko in the third.
But in a match that resumed after rain stopped play following completion of just one game on Monday night, Kohlschreiber looked crisp and confident, breaking the Serbian star for a 4-3 lead in the first and pocketing the set with a service victor on his second set point.
"Didn't he play dubs ... for sure something wrong with him", Kyrgios wrote. "But it is, I guess, part of the world that we are in, the world of tennis". I've got a lot of messages. "So these are the rare occasions where I could potentially do well", Djokovic said.
"I'm very confident with my game right now. So just things worked out for me".
"You can't always make it work". Nadal eased by 25th-seeded Diego Schwartzman 6-3, 6-1, while Federer defeated Swiss countryman Stan Wawrinka 6-3, 6-4. "I had to get over it in an hour, because I played doubles", said Djokovic, cracking a smile.
Poland's 67th-ranked Hubert Herkacz upset sixth-seeded Kei Nishikori of Japan 4-6, 6-4, 6-3 to reach the last 16 of a Masters 1000 event for the first time.
The 22-year-old will next face Canadian teenager Denis Shapovalov, who continued his run of dominant serving without being broken on his way to an impressive 6-4 6-2 win over 10th seeded Croat Marin Cilic.
Tesla to unveil Model Y SUV as electric vehicle competition heats up
Shares of Tesla are down 24 percent from a year high of $379.57 in August, when Musk tweeted that he was taking Tesla private. Some versions will have up to 300 miles of range - which will equate to roughly 480km here in Australia.