17-year-old Prasad defeated Kosie Tanaka of Japan to make it to the semi-finals while Sandeep beat Azizjon Mamatov of Uzbekistan to ensure podium finish at the Championships. Both boxers are now assured of at least a bronze medal.
Prasad, who until now had not really been challenged in the competition, faced some tough opposition from the Japanese boxer in a thrilling contest.
The Indian adopted a cautious approach in the first round, deciding to measure his opponents first. The Japanese also employed a similar strategy waiting for Prasad to make the first move.
With both boxers relying more on counter attacks, the first round ended at three points apiece. A fine display of controlled aggression coupled with some swift footwork saw Prasad win the second round with a crucial one point lead (5-4).
In the final three minutes of the bout, Tanaka tried hard to get back into the game, but Prasad put up a solid guard and kept taking points of his own before winning the bout 12-11.
Prasad is now pitted against Cuban Andy Cruz Gomez in the semi-finals on Thursday.
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Sandeep, a bronze medallist at the 2010 International Invitational tournament in Kazakhstan, overpowered Mamatov in a one-sided affair to make his place in the last four of the middle weight division.
He dominated the bout from the start to the finish never allowing the Uzbek boxer even a fleeting chance to get ahead. By the end of the second round, Sharma had already gained an eight point lead (13-5). He further stretched the gap in the last three minutes to eventually win on points 18-7.
The 17-year-old Haryana lad now fights European Youth Championships silver medallist Magomed Madyiev of Russia on Thursday for a place in the finals.