Nagal hardly moved a sinew in crushing Thailand's Palaphoom Kovapitukted 6-0 6-1 in the second round of the men's singles event.
Riya, the reigning national champion, brushed aside the challenge of Samoa's Steffi Carruthers 6-4 6-2 in the second round of the women's singles event.
Riya had double bageled Rosalie Molbaleh yesterday in her tournament-opener.
Second seed Nagal next faces seventh seed Chun Hun Wong from Hong Kong while Riya will take on Thai fifth seed Cheapchandej.
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Katherine is ranked outside top-1000 but has won two ITF singles titles and incidentally, she won both her trophies in India -- Kolkata in 2012 and New Delhi in 2013.
"I was ready for it (tough fight). Since it was first match and out of the whole draw it was a strong first round so I just stayed strong and I'm glad I pulled it off," Ankita, ranked 260 in the world, told PTI.
"Initially I was trying to pull her wide on both sides and make the court open for down the line but then she got used to it and move early.
"In the third set I kept more cross and once I got a chance, I attacked. I did have a chance in the second set to break her serve and get a lead of 3-1 but that's just because I was 30-0 up and then I lost that game and next I lost my serve which kind of took it to the third set," she explained.
India's women team coach Ankita Bhambri, a former national champion, said the competition will get tougher from quarter-finals onwards.
"Ankita got a good tough first round. That girl is not ranked higher since she plays college tennis but she was very good," Bhambri added.