Sitwala whipped Ryan Mears of England 702-134, Advani routed Martin Schmidt of Austria 874-147 and Geet Sethi virtually toyed with England rival Jonathan Evans in a 687-168 win.
However, another India stalwart Devendra Joshi lost the opening tie narrowly to Michael Pearson of Australia 403-446, according to information available here.
National women's champion Arantxa Sanchis started on a losing note, beaten by Mears 206-368.
The newly-formed World Billiards Limited has brought together the International Billiards and Snooker Federation (IBSF) and World Professional Billiards and Snooker Association (WPBSA) events for a first-ever unified world Championship.
Till last year, there were two different bodies - IBSF and WPBSA - which were organising three different world championships.
Nine cueists took part in the qualifying stage and Indian duo of Manish Jain and Jaiveer Dhingra along with Englishmen Martin Goodwill and Ian Williamson gained berths in the draw. Goodwill defeated India's Alok Kumar to make the grade.
For the first time, 18 Indian cueists are taking part in the world championship which has attracted 65 players from 15 nations.
Results of Indian players: Dhruv Sitwala bt Ryan Mears 702-134; Arun Agarwal bt Phil Mumford 540-317; Nalin Patel bt Derek O
