The top-seeded Serb overcame a double break early in the second set to advance to Friday's semi-finals, where he will play Juan Martin del Potro.
Djokovic won the Wimbledon title in 2011, but lost to eventual champion Roger Federer in last year's semi-finals.
Del Potro overcame an early injury to beat David Ferrer 6-2, 6-4, 7-6.
Del Potro hurt his already injured left knee on the fifth point of the match, and called for a trainer to check it out. But he stayed in the match and quickly took command against the fourth-seeded Ferrer, who was trying to reach the Wimbledon semi-finals for the first time.