After looking less than convincing in his opening round match against America's Robby Ginepri, the world number three put in a much stronger performance against Zib despite making another uneven start.
Playing in his first ATP tournament since losing in the US Open final to Roger Federer on Sept. 9, Djokovic broke Zib in the opening game before suffering an immediate re-break.
From that point onwards the Serb was in total control, twice more breaking the world number 126 without ever being taken to break point himself.
Djokovic, who beat Zib 6-3 6-4 in the first round of the same tournament last year, will now face Argentine seventh seed Juan Ignacio Chela for a place in the semi-finals.
Chela faced an unexpectedly tough challenge from Austrian world number 49 Juergen Melzer in his own second round match, eventually winning 4-6 6-3 6-2.
"I played better than in the first round but I am still not at my best," Djokovic said after securing his quarter-final berth. "I really thought that Melzer would be my next opponent but Chela played fantastically, particularly in the third set so you cannot underestimate him."
Melzer's compatriot Stefan Koubek also raised local hopes of a home-grown quarter-finalist before succumbing 6-4 3-6 6-4 Spain's Fernando Lopez.
Lopez, who beat Austria's Werner Eschauer in the opening round, will now take on Switzerland's Stanislas Wawrinka in the last eight.
Wawrinka upset former Wimbledon finalist and current world number 22 David Nalbandian 5-7 6-3 6-1.
The Swiss number two now boasts a 3-2 head-to-head record against Nalbandian following two wins and two defeats against the Argentine in 2006.