Vikas, a World Championship bronze medallist, outpunched Belarus' Dauhliavets Yauheni 13-2. He will now take on Cuba's Despaigne Arisnoide in the semifinal.
Shiva, who has been picked in the team for next month's Asian Olympic Qualifiers in Kazakhstan, defeated Hungary's Nagy Kriztian 11-3. The promising Assam-lad will now face Czech Republic's Velky Patrik.
"Both these boxers fought extremely well. Vikas was exceptional with his footwork and seems to be gaining in strength as well. Shiva, on the other hand, displayed sharp reflexes and tired out his opponent," coach Jagdeep Hooda, who is with the team, said.
"Although the competition features just about 18 teams, it is the quality of boxers which makes it tough. There are some excellent pugilists from countries like Russia, Italy and Cuba competing here," he added.
But there was disappointment for other Indians is fray, who lost their opening bouts.
The Olympic-qualified duo of Jai Bhagwan (60kg) and Manoj Kumar (64kg) and Sumit Sangwan (81kg), who will represent India in the Asia Olympic qualifiers, lost in the first round itself.
The women drew a blank in the event with Asian Games bronze medallist Kavita Goyat (75kg), Van Lal Duati (51kg) and Preeti Beniwal (60kg) losing in the first round of their competition.
The tournament, being organised by Czech Boxing Association, features over 130 boxers.