It was a positive start for the eventual winner as he grabbed a break point at the first time of asking and immediately held to take a 2-0 lead in the first set.
A further two breaks of serve ensured that Stepanek eased through the opening set, while Youzhny failed to get one game on the board.
Stepanek broke his opponent in the first game of the second set, but this time, Youzhny, ranked 15 in the world, responded by grabbing a break of his own.
However, it was short-lived as Stepanek broke back immediately to keep himself on top and eventually grab a two-set lead.
Youzhny responded in the third set as he reduced the arrears, before serves and breaks were then traded on a frequent basis in the fourth set.
As it was, world number 40 Stepanek came out on top to secure his spot in the next round, where he will face Ernests Gulbis.