Nadal, 20, defeated former world No. 1 Aussie Lleyton Hewitt 6-2, 5-7, 6-4, 6-2. He won in 3 hours, 17 minutes on his second match point of the day when Hewitt sent one final return long.
Hewitt committed six double faults, including five in the fourth set.
Nadal extended his clay court-record winning streak to 57 straight, including 21-0 this year. His quarterfinal opponent on Wednesday will be Serb Novak Djokovic.
Nadal is 32-3 this year, including an ATP-co-leading four titles. World No. 1 Roger Federer also owns four 2006 championships, but is 0-3 in his 2006 finals against Nadal.
Ljubicic earned his 38th match victory of the year by defeating Spaniard Ruben Ramirez Hidalgo 6-3, 3-6, 6-3, 6-2. Only Federer (42) has won more matches than the 6-foot-4 Croat this year.