Still fiercely competitive at the age of 39, Djokovic is looking to equal Roger Federer's tally at the All England Club and go past Margaret Court in the all-time list of Grand Slam titles, and he showed flair and fight to stay on track.
After shedding the custom Lacoste blazer he wore onto Centre Court, Djokovic got down to business, easing through the opening set and still finding time to acknowledge a successful marriage proposal in the stands with a heart-shaped gesture.
Wu, who returned to Grand Slam action this year after two injury-hit seasons, raised his level to snatch the second set and kept up the pressure for eight games in the next before Djokovic broke him and edged ahead in the contest.
Djokovic huffed and puffed in the fourth set before breaking for a 5-4 lead when Wu fired an overhead long, and the Serb duly wrapped up the physically draining match on serve to win 6-4, 5-7, 6-4, 6-4 and set up an intriguing meeting with Stefanos Tsitsipas.