The Belarusian star Azarenka leveled helpless Italian Alberta Brianti 6-0, 6-1 in 67 minutes on the indoor hardcourts at CK Sportcenter Kockelscheuer.
Azarenka's quarterfinal opponent on Friday will be veteran Czech left-hander Iveta Benesova.
The fifth-seeded Serbian Ivanovic, meanwhile, succumbed to British qualifier Anne Keothavong 6-3, 6-1 in 74 minutes on Day 4. Ivanovic captured this event back in 2007.
In other second-round action, Dutch qualifier Bibiane Schoofs landed in her first-ever WTA quarterfinal with a 1-6, 6-1, 7-5 victory over Canadian Rebecca Marino, Latvian Anastasija Sevastova stifled Romanian Simona Halep 6-2, 6-2, and Czech lucky-loser Lucie Hradecka humbled Romanian qualifier Alexandra Cadantu 6-3, 6-4.
Friday's other quarters will pit sixth-seeded German Julia Goerges against Sevastova, Hradecka versus Romanian Monica Niculescu and Keothavong against the 23-year-old upstart Schoofs. Goerges lost to Italian Roberta Vinci in last year's Luxembourg finale.
The 2011 Luxembourg titlist will collect $37,000.