And he is 11-8 against Andy Murray, the fourth of the sport's male quadrangle of champions. Murray is also still alive here.
Djokovic's side of the bracket, now that he has survived the unexpected in Gonzalez, appears to be a clear path. He is the only player in the top 10 there.
With each Djokovic advancement comes a boost for the sport. For the informed tennis fan, his game is special. He covers the court effortlessly, serves big but also with a variety of speed and kicks, and has a mind that produces moments such as the drop shot against Gonzalez.
"I have been in these situations before," he said, referring to what he called a lapse in concentration that got him into the fix Tuesday. "I at least recognize what the issue is, and I need to work on it."
Djokovic brands the sport almost better than anybody, certainly close to the level of the already legendary Federer. Djokovic has been profiled on "60 Minutes," has appeared on Jay Leno's show and with Jimmy Fallon, has been in music videos and had songs written about him. He does charity work and is not bashful about taking an occasional political stance.
He speaks five languages — Serbian, English, German, Italian and French.
Shortly after he made his rise in tennis, he dazzled millions on a telecast of the U.S. Open, where he did impersonations of Nadal, Maria Sharapova and John McEnroe. When he mimicked Nadal's tug at the underpants, Sharapova's pre-point conversations with herself and McEnroe's quirky sideways service motion, a star was born.
Tuesday, at this important and prestigious U.S. tennis event, the star remained, despite a scary blink or two along the way.