Sixth seed Paradorn is in line to face French fourth seed Richard Gasquet in the quarter-finals of the pre-Wimbledon grasscourt event after the teenager beat Czech Tomas Zib 7-6, 6-2 in their first-round match.
The unseeded Ivo Karlovic, who reached the Stella Artois Championships final last week, continued his Wimbledon preparations with a 6-4, 6-4 win over Russian Igor Andreev.
The tall Croat now faces compatriot and top seed Ivan Ljubicic, who put out Romanian Victor Hanescu 6-7, 6-3, 7-6.
At the other end of the draw, second seed Thomas Johansson of Sweden ousted Russian Dmitry Tursunov 7-6, 6-3.
