World number five Zverev, 20, is the highest-ranked player left in the draw of the hardcourt tournament.
Maria Sharapova was sent crashing out of the Australian Open in a crushing defeat by Angelique Kerber Saturday as Simona Halep survived a titanic struggle to make the last 16.
Jack Sock is the first American to reach the semi-finals of the ATP World Tour Finals event since Andy Roddick in 2007.
The world number two saw off a spirited challenge from the much-hyped German 7-6 (8/6), 5-7, 6-1 in front of a boisterous pro-Federer crowd to become the first man through to the last four at the O2 Arena.
Zverev, at 20, should have been among the line-up in the under-21 version of the ATP Tour Finals but his stunning season has already earned him a ticket to play with the big boys in London.
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.
Roger Federer introduced Rafael Nadal for the Laver Cup and the Spaniard's reaction to it was just pure gold.
With four matches a day -- three singles and a doubles, the players can earn a point for each win on Friday, two on Saturday and three on Sunday.
Maria Sharapova, ranked 146th, played only one US Open tuneup match due to a forearm injury but wore down Simona Halep and Babos to prove she's a threat for a deep run.
Next for Rafael Nadal, who had a first-round bye, is a third-round matchup with 24th-ranked countryman Albert Ramos-Vinolas.
The Indo-German pair went down to the Spanish Duo of Feliciano Lopez and Marc Lopez 2-6, 7-6 (7-2), 10-6.
20-year-old Alexander Zverev halts Roger Federer's win streak at 16.
Roger Federer outclassed Roberto Bautista Agut in straight sets to inch closer to his sixth title of the season.
Federer, who is aiming for an eighth Wimbledon crown, won 6-1, 6-3 in just 53 minutes.
Rome Masters winner Zverev shocked by Fernando Verdasco but world No 1 Murray and former French Open champion Wawrinka advance to the second round.
Alexander Zverev will move to No 10 in the world after winning the Masters title in Rome.
Novak Djokovic overcame having to play twice in a day before cruising into his eighth final of the Rome Masters with a ruthless 6-1, 6-0 win over Dominic Thiem on Saturday.
Rafael Nadal needed all his trademark grit against Alexander Zverev, 19, dubbed "the future of tennis", and his superior fitness told as he ground out a thrilling 4-6, 6-3, 6-7 (5/7), 6-3, 6-2 win