In brutal temperatures, the Japanese 16th seed kept the match to just one hour 49 minutes before prevailing 6-1, 6-1, 7-6 (7/3) over the Serb.
Nishikori, 24, now coached by former French Open champion Michael Chang and playing in heat of 41 Celsius (106 Fahrenheit), reached the third round for the fourth consecutive year.
"I think I felt much hotter than the first day I played," Nishikori said. "I finished early today so it helped my body."
Nishikori was on court for three hours 41 minutes before subduing Australian Marinko Matosevic in a five-setter in Tuesday's opening match.
"I was playing amazing, actually. In the first and second sets I was playing really aggressive, big forehand, and serve as well," he said.
"But he started coming back, he was playing a little better and I'm very happy to finish the tiebreak strongly."
It was a polished performance by the Japanese star, who broke the Serb's service six times and was only broken once, in the eighth game of the final set.
Nishikori was particularly strong on his forehand with 16 winners among his overall total of 30 winners, while conceding 27 unforced errors.
It set up Nishikori with a third-round encounter against either Italian 24th seed Andreas Seppi, who knocked Australia's Lleyton Hewitt out in the opening round, or American Donald Young.
Nishikori, who beat Tomas Berdych in the Kooyong Classic final last weekend, enjoyed his best Grand Slam result two years ago in Melbourne when he reached the last eight.