Runners-up in the snooker nationals this year, Chawla, 34, held his nerve to beat Jordan's Lailth Alnaser 4-3 in the round-of-32 clash.
Meanwhile Lilly also got past Funk Kwok Wai (Hong Kong) 4-3 in another interesting match-up.
Lilly, 39, will now take on Chuan Leong Thir of Malaysia in the round-of-16 match while Chawla faces China's Chen Zifan in the pre-quarters tie.
Earlier another Indian in the fray, Brijesh Damani, had crashed out after losing to Baldandorj Batsukh of Mongolia.