Top seed Novak Djokovic came through a dramatic first-set tie-break before prevailing 7-6 (7/5), 6-4 to move to the brink of a record-extending fifth Bercy title.
Rafael Nadal is bidding for a record-extending 36th Masters crown and will take on Denis Shapovalov in the last four.
Novak Djokovic holds an 8-1 winning head-to-head record against Grigor Dimitrov, who saw off unseeded Chilean Cristian Garin 6-2, 7-5 earlier in the day.
Roger Federer, trying to stretch his men's Grand Slam record title total to 21, advanced to a last-eight match up with Bulgaria's 78th-ranked Grigor Dimitrov.
The Japanese had set his sights on returning to the world's top five after falling to 39 last April due to a wrist injury.
Andre Agassi previously coached Novak Djokovic from the 2017 French Open until they split in March this year.
Team World slashed Europe's overall lead to 7-5 heading into Sunday's third and final day of the 2018 Laver Cup.
Novak Djokovic is aiming to lift the trophy at the only one of the Masters 1000 series events that he has never won.
Novak Djokovic is vying to break through for a first Cincinnati Masters win after coming up empty in five finals.
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.