'I would say after 3-all in the first set I felt like getting closer to the set, holding my service games, which is not easy against Novak, because he's such a great returner, ' Kohlschreiber said. "Of course, playing the top guys is always a big pleasure, but most of the time they beat you", Kohlschreiber said on court.
'I liked my chances more at night against Kohlschreiber, but it wasn't to be last night, ' Djokovic said.
"Today, with Novak being number one, top-seeded here, it's a very incredible win for me".
Nadal eased by 25th-seeded Diego Schwartzman 6-3, 6-1, while Federer defeated Swiss countryman Stan Wawrinka 6-3, 6-4.
In match that resumed after rain stopped play just one game in on Monday night, Kohlschreiber said the warmer daytime conditions suited him better.
Kohlschreiber notched his first ever victory over a number one-ranked player, ending Djokovic's bid for a sixth Indian Wells crown.
He came out with a crisp, confident style, breaking Djokovic in the seventh game and closing out the opening set with a service victor.
Kohlschreiber posted his first victory over a top-ranked player, advancing to a fourth-round match against France's Gael Monfils.
Nadal took his record against the world No. 26 to 7-0 in emphatic style, never facing a break point in a match lasting an hour and 16 minutes. "I must admit I was thinking about it. but it's part of our world, and we just have to bounce back very quickly".
The Serb, who now holds three of the four Grand Slam titles, was beaten 6-4 6-4 by the German world number 39.
On Tuesday, the 23rd-ranked Bencic served and returned better.
"I haven't played that much, so I wanted to make it count", said Williams, who expects to play about 12 tournaments this year.
Federer next faces Britain's Kyle Edmund, who beat Macedonian qualifier Radu Albot 6-3, 6-3.
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.