Zverev is looking to become the first German man to win the title since 1937
Seven-time major winner Venus Williams suffered back-to-back opening-round exits at the Slams for the first time in her 21-year career.
The top seed is bidding for an outright record 31st Masters title this week and extended his run of consecutive sets won on clay to 34.
The Spaniard is now just two wins away from a record 31st Masters title, after winning 32 consecutive sets on clay.
The world number five wrapped up the victory in the breaker on his second match point to claim one of the best wins of his career on clay.
Roger Federer, the oldest No.1 in history, thrashed Bulgarian Grigor Dimitrov 6-2, 6-2 in a one-sided final.
Roger Federer celebrated becoming the oldest man to reach the world number one ranking by making the Rotterdam Open final with a 6-3, 7-6 (7/3) victory over Italy's Andreas Seppi.
Second seed Dimitrov had to fight back in the second set to defeat Japan's Yuichi Sugita 6-4, 7-6 (7/5) in their first-round encounter.
The unseeded Edmund, ranked 49, won 6-4, 3-6, 6-3, 6-4 in 2hr 49min on Rod Laver Arena and will face either 16-time Grand Slam champion Rafael Nadal or Marin Cilic for a place in the final.
Dimitrov downed the 17th seeded Kyrgios 7-6 (7/3), 7-6 (7/4), 4-6, 7-6 (7/4) in 3 hour 26 minutes and will face Britain's Kyle Edmund in the quarter-finals.
Dimitrov, who is ranked only below Rafael Nadal and Roger Federer, drew on all his experience to avoid his first defeat to a qualifier at a Grand Slam.
Grigor Dimitrov will climb to third in the rankings behind only Rafael Nadal and Roger Federer as he begins to deliver decisively on his rich promise as a youngster.
Roger Federer has never lost a single match to any of the remaining players in the ATP World Tour Finals 2017.
Jack Sock is the first American to reach the semi-finals of the ATP World Tour Finals event since Andy Roddick in 2007.
Dimitrov has never quite lived up to his billing as the heir to Roger Federer's throne, but the world number six's eye-catching rout of Goffin was a reminder he is still young and gifted enough to finally make the breakthrough.
Dimitrov, who defeated Dominic Thiem in three sets in his Pete Sampras group opener, has already made history as the first Bulgarian to qualify for the season-ending Tour finals.
The ATP World Tour Finals feature the top eight fit male singles players and doubles teams that have accrued the most points throughout the 2017 season.
The former US Open champion can take the eighth and final qualification spot for London from Pablo Carreno Busta if he reaches the semi-finals at Bercy, and he will face either John Isner or sixth seed Grigor Dimitrov in the last eight.