Asian silver-medallist Vikas (75kg) got the better of European silver winner and fourth seeded Pole Tomasz Jablonski 2-1. Shiva (56kg), on the other hand, rallied to defeat the African champion Mohamed Hamout of Morocco to make the last-eight stage.
The 21-year-old Shiva will next be up against Qatar's Hakan Erseker, who beat Vanuatu's Boe Warawara 2-1. The 23-year-old Vikas, meanwhile, will face Egypt's Hosam Abdin.
"Vikas boxed superbly. The Polish guy was a tempo boxer but Vikas applied his mind well. He used uppercuts to the chin and occasional right hooks with precision," added Sandhu analysing the overall performance.
First up in the ring for India today was Shiva and in a terrific win, the Assam boxer knocked out his rival 26 seconds into the third and final round of the bout with a brutal left hook which landed right in between the eyes of Hamout.
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But it was not as smooth to start with for Shiva. Both the boxers hit attack mode from the first bell itself and in the opening three minutes, the judges ruled in favour of the Moroccan despite an even contest.
However, the Indian, a former silver-medallist from the 2010 Youth Olympic Games, remained relentless in his attack in the second round and drew level via a split decision.
In the decisive third round, Shiva, also a former Asian champion, sealed the issue with a precise left hook, which caught Hamout completely off-guard.
The clean straight hitting got him the scores as Vikas out-ran Jablonski in the first two rounds.
However, Jablonski fought back in the third round and won it unanimously but Vikas emerged the overall winner owing to his early lead.