Youzhny took out Italian Flavio Cipolla 6-3, 6-2.
Romania's Victor Hanescu outlasted the 6-foot-10 Karlovic of Croatia 6-7 (4-7), 7-6 (7-3), 7-6 (13-11).
Karlovic fell despite slamming 28 aces in a battle that lasted just over 2 1/2 hours.
Youzhny and Hanescu moved on to the quarterfinals, along with French qualifier Jeremy Chardy and Spain's Guillermo Garcia-Lopez.
Chardy fired 19 aces and edged another qualifier, Dominik Meffert of Germany, 6-7 (1-7), 7-6 (7-5), 7-6 (7-4). Garcia-Lopez advanced when his opponent, sixth-seeded Nicolas Kiefer of Germany, withdrew because of a toe injury.
In Friday's quarterfinals: Top-seeded Stanislas Wawrinka of Switzerland plays No. 8 Guillermo Canas of Argentina, Youzhny meets Garcia-Lopez, seventh- seeded Russian Igor Andreev takes on Marin Cilic of Croatia and Hanescu meets Chardy.
Celebrity Families of 2014 [PHOTOS]