The third-seeded Youzhny eased past Slovenia's Grega Zemlja, 6-1, 6-3, and is now the highest seeded player remaining. Top-seeded Ivan Ljubicic was beaten in the second round on Wednesday and Bogomolov was the second seed.
Lacko dominated early and late in a 6-0, 6-7 (1-7), 6-1 win over Bogomolov. He won the first nine games of the match before Bogomolov rallied in the second set. However, 2011's most improved player could not sustain the momentum in the third.
Next up for Lacko will be seventh-seeded Dutchman Robin Haase.
The fourth-seeded Dodig needed three sets to dispose of Spain's Guillermo Garcia-Lopez, rallying for a 4-6, 6-4, 6-4 triumph. Dodig, a native Croat, will next face Baghdatis, who moved on with a 6-4, 6-2 victory over Poland's Lukasz Kubot.
Baghdatis will play in his third quarterfinal of 2012, having already reached the round of eight at the Australian Open tuneup in Brisbane and the semifinals in Sydney.
Friday's remaining quarterfinal will feature Austrian veteran Jurgen Melzer against German Michael Berrer, both second-round winners on Wednesday. Melzer knocked off fifth-seeded Andreas Seppi and Berrer took out Ljubicic.
Berrer lost to Dodig in last year's Zagreb final.
This week's champion will collect $90,000.