Second seed Sumit defeated compatriot Virender Kumar 5-0 but sustained a cut above his eye, which might force him to skip the semifinals.
Sarjubala Devi (51kg) and Pinki Jangra (51kg) advanced to the semis in the women's competition.
The heavyweight (91kg) top seed, Naman Tanwar, who claimed a bronze at the world youth championships, made an impressive debut in the senior circuit, defeating Jordan's Eishaish Hussein to enter the semifinals and be assured of a medal.
Shiva will face Uzbekistan's Sherbek Rakhmatulloev tomorrow.
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Another impressive win of the day was notched up by reigning national champion Manish Kaushik (60kg), who came up with a spirited show to defeat Cuba's Rabi Armando Martinez.
Top seed Sarjubala assured India of their first medal of the day when she got past Kenya's Christine Ongare 5-0.
The diminutive Manipuri, who is a world championships silver-medallist was in aggressive mode from the first ring of the bell.
She set up a semifinal clash with Mongolian Jargalan Ochirbat, who upstaged 13the seed and former junior world champion Nikhat Zareen in a fiercely-contested clash. Ochirbat won the bout on a split 3-2 verdict.
Also advancing to the medal rounds was Commonwealth Games bronze-medallist Pinki Jangra (51kg). She scored a comprehensive 5-0 triumph over Jordan's Al-Mriheel.
Among the men, world championships quarterfinalist and Asian bronze-medallist entered the last-eight stage without having to fight after his rival Ramish Rahmani of Afghanistan gave him a walkover.
Mavia will square off against another Indian in Shaikh Salman Anwar.
Next up for Amit is Cameroon's Fotsala Simplice, who got the better of Malaysian Mohammad Fuad Bin Redzuan.
King's Cup gold-medallist K Shyam Kumar (49kg) also advanced to the quarters but after a draining contest against compatriot Neeraj Swami even though the scoreline read 5-0 in favour of the former.
Asian youth silver-medallist Ashish (64kg) scored an impressive triumph over Kazakhstan's Sabyrzhan Abilov to continue India's dominance in the tournament. Ashish won on a split verdict.
Earlier, Pooja (69kg) had been assured of a medal after making the semifinal straightaway owing to the small size of her draw.
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