Shiva, a former Asian champion, started the proceedings on a perfect note for the country as he outpunched Algeria's Khalil Litim 3-0.
The 23-year-old will next face Morocco's Mohamed Hamout, who got a first-round bye.
Later, Vikas also sailed past Hungary's Zoltan Harcsa 3-0 to make the last-16 stage. Vikas has a very tough bout next up as he will be up against fourth-seeded Tomasz Jablonski, a European Championships silver-medallist.
"Both Shiva and Vikas dominated their bouts in the first two rounds and took it easy in the third for obvious reasons. They have tough opponents in the next round but fingers crossed for a good result," national coach Gurbax Singh Sandhu told PTI.
However, it was curtains for Manoj Kumar (64kg) in the very first round as he was stunned 1-2 to Moroccon Abdelhak Aatakni.
His movement sluggish in the first two rounds, Manoj gathered himself in the final three minutes but the comeback was a tad too late as Aatakni clinched the bout.
