Ljubicic, seeded third and bidding to win the Vienna Open for a third successive year, was beaten 6-3 6-3 by Italian world number 73 Andreas Seppi.
Gonzalez was then defeated 6-3 4-6 6-4 by Spanish former world number one Juan Carlos Ferrero.
Top seed Djokovic faced a scare of his own, defending two match points before eventually seeing off Argentine seventh seed Juan Ignacio Chela 6-3 5-7 7-6.
Djokovic will now face Seppi in the semi-finals while Ferrero takes on Switzerland's Stanislas Wawrinka, a 6-7 6-3 6-4 winner over Spain's Feliciano Lopez in the day's remaining quarter-final.
Ljubicic's defeat was probably the biggest shock of the day with Seppi handing the Croatian his first ever loss in the Austrian capital.
The world number 13, who won the Vienna title in 2005 and 2006, was broken three times during a surprisingly one-sided encounter.
"He probably made more unforced errors than normal today but hopefully one of the reasons for that was that I was able to put him under some pressure," Seppi said.
"Seppi played fantastic tennis today," the departing champion acknowledged.
"Nothing I was trying out there seemed to work but I can assure you I was doing all I could to get back in the match."
RESOLVE
Ferrero showed strong resolve in his meeting with Gonzalez, throwing away the second set after dropping serve in the last game but recovering with an immediate and decisive break of the Chilean's serve at the start of the third set.
It was the Spaniard's second win over Gonzalez this year and his third match of the week to go to three sets.
Djokovic was grateful to avoid a similar upset after finally wrapping up victory over Chela in just under three hours.
"I just had a bit of luck on the important points because I was very close to going out," the 20-year-old Serb said.
Apparently cruising after taking the first set and then breaking ahead to 4-2 in the second, Djokovic was caught off guard as Chela mounted an impressive fightback.
Winning five of the next six games to secure the second set, the Argentine then had two match points as Djokovic served at 4-5 down.
The world number three saved the first with a gutsy run to the net and the second with a service winner before going on to clinch the deciding tie-break 7-2.
(Writing by Mark Ledsom in Berne)
