Badami, who came through the round robin untroubled, endured a late challenge before stopping city rival Pawan Kohli of Khar Gymkhana with a 60-28, 73-13, 53-63, 29-54, 59-35 win at the National Sports Club of India here.
Badami got off to a good start with a 2-0 lead that included a break of 42 in the opening frame. But Kohli fought back brilliantly to force the decider before bowing out.
D'Souza rallied after losing the opening frame to a 2-1 lead but Kulkarni kept his hopes alive by snatching the crucial fourth frame. A break of 44 by D'Souza proved decisive in the fifth and final frame, leaving his rival with no chance to recover.
Asian 6-Red bronze medallist Laxman Rawat and former Maharashtra state junior champion Jaiveer Dingra of P J Hindu Gymkhana were the other notable players to rally their way into the last eight.
Dhingra struggled against Dhariya Bhandari, also of ISA, en route to a 3-1 win after dropping the third frame narrowly and snatching the crucial fourth on the black when Bhandari missed the blue and pink and an opportunity to force the decider.
Pranit Ramchandani of Tamil Nadu ended the campaign of Rajwardhan Joshi of PYC Hindu Gymkhana with a 3-0 win, while host state's junior and sub junior champion Ishpreet Singh Chadha stopped the progress of Karan Chugh of host club NSCI with a 3-1 win.