Djokovic, of Serbia, had only 11 unforced errors while cruising to a 6-2, 6-1 victory over Spain's Roberto Bautista Agut.
"I wanted to be aggressive and it's what I've done," Djokovic told reporters. "The conditions were quite different than (Wednesday). It was a bit slower but a bit more windier, so I had to be concentrated."
Murray, the American defending champion, dispatched of Gilles Simon of France 6-4, 6-2.
"I didn't return that well at the beginning," Murray said. "But when I got into a rhythm, I was able to dictate a lot of points. I used my variety well and served well. He wasn't able to put me under much pressure on my serve after the first couple of games."
In other men's matches, sixth-seeded Kei Nishikori of Japan defeated 10th-seeded Richard Gasquet of Switzerland 6-4, 7-5; eighth-seeded Thomas Berdych of the Czech Republic was a 7-6 (8), 7-5 winner over ninth-seeded David Ferrer of Spain, and Australian Nick Kyrgios defeated Uruguay's Pablo Cuevas 7-6 (5), 4-6, 6-3.
In women's quarterfinal action, sixth-seeded Simona Halpe of Romania defeated countrymate Irina-Camelia Begu 6-3, 0-6, 6-1. Slovakia's Dominika Cibulkova defeated Romania's Sorana Cirstea 4-6, 6-3, 6-3, and American qualifier Louisa Chirico was a 7-6 (1), 6-2 victor over Russia's Daria Garilova.
The 19-year-old Chirico became the first American teenager to advance to the semifinals of a high-quality clay-court event since Ashley Harkleroad in 2003.