While holder Rafa Nadal of Spain and fourth-seeded Briton Andy Murray both advanced, second seed Djokovic was eliminated in a match lasting one hour and 44 minutes.
The Serbian world No. 2, winner here in 2008, lost his serve in the sixth game of the second set and sent a forehand service return long to hand Ljubicic victory.
Ljubicic, the 20th seed, fired down 13 aces in the searing desert sunshine to record only his second win against Djokovic in seven meetings.
"I had a lot of opportunities and I didn't use many of them," Djokovic told reporters after converting only two of five break point chances. "My execution was very bad and he played well when he needed to." Although the 6ft 4in (1.93m) Ljubicic lost serve in the third game of the match, he broke back in the eighth and 12th to take the opening set in just under an hour.
Repeatedly unleashing first serves above 130 mph; he swept through the second set to book a place in the quarterfinals against 21st seed Juan Monaco of Argentina, who beat Spaniard Guillermo Garcia-Lopez 3-6, 6-2, 6-1 earlier in the day.
Nadal overcame towering American John Isner 7-5, 3-6, 6-3 and Murray advanced after Spaniard Nicolas Almagro retired hurt with a left ankle injury when trailing 6-2, 1-0.
Twice champion Nadal, who beat Murray in last year's final, broke the six-foot-nine Isner in the fourth game of the third set before sealing victory with a forehand winner down the line.
The Spanish left-hander leaned backwards in delight to celebrate his advance to the last eight where he will play Czech Tomas Berdych, who crushed Serbia's Viktor Troicki 6-1, 6-3.
Seventh-seeded American Andy Roddick needed just one break of serve to beat Austrian Juergen Melzer 7-6, 6-4 in a tight match and will next meet Spaniard Tommy Robredo, who battled past Baghdatis 7-5, 0-6, 6-4.
Sixth seeded Swede Robin Soderling brushed aside Frenchman Jo-Wilfried Tsonga 6-3, 6-4 and will face Murray in the last eight.
In the women's section, Caroline Wozniacki resisted a sizzling baseline display from China's Zheng Jie to reach the semifinals with a hard-fought 6-4, 4-6, 6-1 victory on Wednesday.
The second-seeded Dane, who had been beaten by Zheng in their two previous meetings, broke her opponent three times in the final set to win the match in two hours 18 minutes.
Wozniacki, at 19 the youngest player left in the tournament, let out a shriek of delight after 18th-seeded Zheng pushed a backhand wide to end a fluctuating encounter of high quality.
Wozniacki will next meet her good friend Agnieszka Radwanska of Poland, who breezed into the last four with a 6-4, 6-3 victory over fourth-seeded Russian Elena Dementieva.
Radwanska, who has yet to drop a set at Indian Wells, broke her opponent twice in each set to win the match in one hour 31 minutes.
