The top half of the draw has already lost world number one Andy Murray and offers rather smoother sailing than a bottom half, which features multiple grand slam winners Novak Djokovic, Rafa Nadal and Roger Federer.
Wawrinka needed just 78 minutes to improve to his career record against Germany's Kohlschreiber to 5-0, whipping a trademark backhand winner down the line to end the third round contest at Indian Wells.
"I was serving well," the 31-year-old said. "I think I'm moving better and better, and it's all positive so far.
"I'm feeling good in my body, so that's the most important."
Nishioka, who gave Nadal a run for his money in Acapulco at the start of the month, surprised even himself with his victory over Berdych.
"I tried to do my best, but today I couldn't figure out how could I beat Berdych," Nishioka said. "I tried to find a way, and then I think he give me a little bit of a chance.
"My body was feeling like I cannot move that much, but I just stayed focussed and tried to fight. And then I found a way."
Berdych held match point on Nishioka's serve in the 10th game of the second set, before the Japanese rallied to level the contest in a tie-break.
After trading breaks at the start of the decider, Nishioka broke again for a 2-1 lead and did not look back.
Eighth seed Dominic Thiem of Austria made it through to the fourth round by beating Mischa Zverev 6-1 6-4 in less than an hour.
Two days after ousting top seed Murray, Vasek Pospisil's run in Indian Wells came to an end as he fell to fellow qualifier Dusan Lajovic of Serbia 6-7(4) 6-3 7-5.
Pospisil served for the match at 5-3 in the third set but was broken to love and the Canadian also squandered a match point in the 10th game before Lajovic prevailed.
Lajovic, ranked 106, will face Pablo Carreno Busta, who earned a free pass into the fourth round after fellow Spaniard Roberto Bautista Agut withdrew before their match due to an abdominal muscle injury.
(Reporting by Larry Fine in New York; Editing by Nick Mulvenney)
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