US-based Malhotra, ranked 125th in the world, warmed up with a promising start by winning the opening game in the best-of-five contest, before Kumar came back to win the next two in one of the most exciting matches of the day.
But Malhotra, recent winner of the Malaysian Tour 2016 Leg I, the Florida State Open and runner-up at the Samson Seattle Squash Open, grabbed the crucial fourth in a tight finish before holding on to a marginal lead in a close decider to set up a clash with defending champion Saurav Ghosal.
Third seed Sachika Ingale of UP recovered from 0-2 to snatch the decider over extra points in a thrilling women's pre-quarterfinals against Aishwarya Bhattacharya.
Staring at defeat, Ingale relied on experience to get back into the match by clinching the third and fourth games to force the decider.
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In a contest that could have gone either way, a determined Aishwarya stretched her accomplished opponent all the way in a neck-to-neck final game before Sachika took it away.
Vijay Kumar (TN) 11-8 11-2 11-6; Vikram Malhotra (Mah) bt Kush Kumar (TN) 11-5 8-11 10-12 11-9 11-7; Harinderpal Singh Sandhu (TN) bt Ravi Dixit (TN) 11-6 11-7 11-3; Mahesh Mangaonkar (Mah) bt Velavan Senthilkumar (TN) 11-4 11-6 11-6.
Women (Quarter-finals): Joshna Chinappa (TN) bt Jui Kalgutkar (Mah) 11-5 11-6 11-4; Akanksha Salunkhe (Goa) bt Urwashi Joshi (Mah) 12-10 11-9 11-5; Sachika Ingale (UP) bt Adya Advani (Del) 11-5 11-4 11-8; Dipika Pallikal Karthik (TN) bt Lakshya Ragavendran (TN) 11-3 11-4 11-4.
Pre-quarter-finals: Joshna bt Ananya Dabke 11-6 11-3 11-5; Jui bt Jannat Duhan (Chg) 11-5 11-0 11-3; Urwashi bt Mayuri Namasivayam (TN) 11-6 11-5 11-4; Akanksha bt Aishwarya Khubchandani 11-7 11-5 11-3; Sachika bt Aishwarya Bhattacharya 13-15 9-11 11-7 11-0 14-12; Adya bt Aryaa Ogale 11-4 11-6 11-3; Lakshya bt Anannya Morey 11-2 11-5 11-7; Dipika bt Avani Nagar 11-2 11-1 11-3.