"I thought I was in good form". We beat a very experienced doubles team."Djokovic and Fognini are the first team into the semi-finals in the California desert, triumphing after one hour and 36 minutes".
Kohlschreiber will face France's Gael Monfils for a place in the quarter-finals.
The match between Djokovic and Kohlschreiber began on Monday but was delayed until Tuesday because of heavy rain.
Serbia's Djokovic, who now holds three of the four Grand Slam titles, was beaten 6-4, 6-4 in his third round match at the Association of Tennis Professionals (ATP) event against Germany's world number 39 Phlipp Kohlschreiber. "I think I played a very, very good game today, and beat a rival who is an unbelievable player and who started the season really well so I'm happy for that and excited for the next one".
Bencic, the 23rd seed from Switzerland, is on a roll, winning 11 straight matches and beating Top 10 players in her last five matches.
"I congratulate him for playing tactically really well and getting me out of my comfort zone", Djokovic said.
Nadal, a three-time champion at Indian Wells, did not face a break point in the match. "I'm not at my highest level, I know that, but hopefully I'll be able to peak in Miami". I don't play often.
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She will face resurgent Swiss Belinda Bencic , a 6-4, 6-2 victor over Ekaterina Alexandrova of Russian Federation . Halep got injured during the match and received treatment for blisters on her foot.
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"[It's] not easy mentally to refresh your mindset and concentration and get the right intensity on the court so quickly after disappointing loss in singles".
Nadal, a three-time victor of the Indian Wells title, next faces Serbian qualifier Filip Krajinovic, who ousted 14th-seeded Russian Daniil Medvedev 6-3, 6-2. Nadal eased by 25th-seeded Diego Schwartzman 6-3, 6-1, while Federer defeated Swiss countryman Stan Wawrinka 6-3, 6-4.
"She forced the issue on every point, didn't make a lot of errors, played defensively when she had to, played offensively", Williams said of her German opponent, ranked No. 97.
"When I hit a good return, I was wondering why this didn't happen in singles. So just things worked out for me".
In women's fourth-round matches, No. 2 Simona Halep lost to Marketa Vondrousova 6-2, 3-6, 6-2; and No. 7 Kiki Bertens was beaten by 20th-seeded Garbine Muguruza 5-7, 6-1, 6-4.
He will play 19-year-old Canadian Denis Shapovalov, the 24th seed who beat 10th-seeded Croatian Marin Cilic 6-4, 6-2.
Venus Williams is into the quarterfinals with a 6-4, 6-4 win over Mona Barthel.
In his on-court interview, when asked how it felt to see his hard work still paying off at this stage of his career, the 35-year-old German joked to laughter and applause, "What do you mean, this stage?"