Amalraj-Madhurika, who got a bye in the first round, defeated Mongolian pair of Orgil Munkh Batbayar and Enkhjin Barkhas 3-0 (12-10, 11-3, 11-6) in just 13 minutes.
Sluggish to begin with, the Indian team was stretched and had to work hard before taking the first game 12-10.
The Indian team played with much more discipline and confidence in the next two games.
They got into a fine rhythm and wrapped up the next two games 11-3, 11-6 in three and five minutes, respectively to progress through to the next round.
The Indian pair will take on Japan's Seiya Kishikawa and Ai Fukuhara in the next round Tuesday.