The unseeded Indian began brilliantly by routing his Latavian rival in the first set only to see a reversal in the following set.
However, Prakash held his nerves and prevailed over Juska in the final set tie-breaker to march into the last-eight stage of the $1,00,000 hard court event.
He will fight it with Dutch Igoi Sijsling, who ousted third seed Lukas Lacko, for a place in the semifinal.
Meanwhile, fourth seed Purav Raja and Sadik Kadir scored an easy 6-3 6-2 win over Greg Jones of Australia and Pavel Snobel of Czech Republic to enter the doubles semifinals. The Indo-Australian pair will face winner of the Andis Juska/ Dmitri Sitak vs Rik De Voest/Frederik Nielsen quarterfinal match.