Youzhny, seeded 20th, beat Viktor Troicki of Serbia 6-3 6-4 7-5 on Saturday to set up a Monday meeting against Britain's number one.
Troicki fired down four aces in the opening set, but Youzhny was able to break serve on his second opportunity to take the opener after just 22 minutes on a sun-baked Court Two.
His Serbian opponent offered more threat in the second set but was unable to take any of the three break points on offer and Youzhny moved within one set of victory.
Troicki started the third set comfortably, holding firm after a series of unanswered serves and big shots from the back of the court. Youzhny then broke, but Troicki hit back.
In the eighth game of the set, Troicki injured his ankle while diving for the ball. The Serbian was soon back on his feet, but his confidence was dented.
Youzhny broke in the 11th game with a brilliant cross-court forehand, which the crowd lapped up.
He then clinched the match with a 116mph ace before embarking on a bizarre celebration that involved balancing his racquet on his head.
Murray should be confident of progressing from Monday's game. Youzhny's movement is good, but he does not possess the power of the second seed.
The Scot has won both of his previous encounters with Youzhny. The first came in St Petersburg six years ago, where Murray won in three sets.
Murray then beat the world number 26 6-3 6-2 in Valencia two years later.