The 22-year-old rising star took the first-set tiebreaker from Carlos Berlocq and then was too strong for the Argentine, winning 7-6 (7-4) 6-4 6-1.
The Open's 16th seed will meet the winner of the all-Russian match between No.23 seed Mikhail Youzhny and Evgeny Donskoy.
Nishikori made history at the Australian Open last year when he became the first Japanese men's player in the modern era to reach a grand slam quarter-final.
He was also the first Japanese player to win his home country's Open in its 41-year history and reached a career-high ranking of 19.
Nishikori made a wobbly start to this month when a left knee injury forced him out of the Kooyong Classic, but he was able to play a practice match before the Australian Open.
Also on Wednesday, Spaniard Nicolas Almagro was the first player through to the men's third round.
The tournament's 10th seed only needed an hour and 41 minutes on day three to beat compatriot Daniel Gimeno-Traver 6-4 6-1 6-2.
The world No.11 has reached the fourth round at the Open for the past three years.
He will play Indian Somdev Devvarman or Polish 24th seed Jerzy Janowicz.
American Sam Querrey lost his first-set tiebreaker to journeyman and compatriot Brian Baker, but Baker then retired at 1-1 in the second.
Querrey will face Swiss 15th seed Stanislas Wawrinka or Tobias Kamke.
-AAP