While Ghosal defeated junior champion Marwan El Shorbagy from Egypt in straight sets, Pallikal fought back from two game deficit to beat another Egyptian, Omneya Abdel Kawy 3-2.
Ghosal had little difficulty in getting past Marwan 11-7 11-6 11-5.
He will now face Peter Barker from England in the round of 16 tomorrow.
"I knew I'd have to play. I tried to be clinical from the start and it worked pretty well. Playing Peter will be tough, but there's no shortage of incentive with a quarter-final in the British Open for the winner, so hopefully I can play well again and it will be a good match," Ghosal said after the match .
In the women's event, Pallikal nearly crashed out of the tournament in round one after going two games down to Kaway, in a fractious and gritty tie.
The Indian star, however, turned it around as the Egyptian's fitness waned to pocket the match 8-11 9-11 11-9 11-5 11-5 in 70 minutes.
Pallikal will take on Raneem El Weleily of Egypt in her next round tomorrow.
"In the first two, I sat back a bit too much, and relaxed a bit too much. I probably thought, I will come back in the second, but you can't do that with a player of that calibre," Pallikal said.
"After that, I used the four corners, varied my angles. And I felt she was getting a bit tired, and stepped back a bit. I was lucky in the third though, I was down and in the fourth too, but at a crucial time, she got a conduct stroke, and that was very important in the match," she added.
