Vani, who is playing her seventh Women's Indian Open but fifth as a pro, used her course knowledge to come back from being two-over after five holes to finish with 69.
She had six birdies against three bogeys and was placed tied-4th along with five others.
Vani was two shots behind leader Norwegian Marianne Skarpnord, who also had six birdies but only one bogey, the result of a three-putt on fifth, in her first competitive round at the Gary Player layout.
Vani was tied fourth with Meghan MacLaren, Klara Spilkova, Olivia Cowan, Karolin Lampert and Kanphanitnan Muangkhumsakul.
Just behind them was defending champion Aditi Ashok (70) and local DLF golfer, Gaurika Bishnoi, who is also the Order of Merit leader on the local Hero Women's Pro Golf Tour.
Among other Indians, Saaniya Sharma (73) was tied-41st, while Gursimar Badwal (74) was tied-54th. However, Amandeep Drall (77), Smriti Mehra (78) and Sharmila Nicollet (79) had a disappointing first day.