Chinappa, who has been in fine form in the last six months, moved a place to be 10th in the standings. Pallikal, who broke the top-10 barrier in December 2012, is ranked 19th in the latest rankings.
Chinappa had reached her biggest ever final at the HKFC International in Hong Kong in May.
She is now getting ready to defend her title in the National Championship, to be held in Mumbai from July 12.
Pallikal, who was 18th last month, dropped a place in the rankings. She was a quarterfinalist at the HKFC International.
The only other Indian in the top 20, Saurav Ghosal, remained on 17. Ghosal had been off action for a while nursing an ankle injury and is due to return to active squash at the Nationals in Mumbai.
PTI