The 33-year-old Frenchman did not disappoint his home crowd as he beat the Croatian in three sets 1-6, 6-3, 6-2 to reach the final of the tournament.
Top seed Marin Cilic from Croatia outplayed Pierre-Hugues Herbert while Kevin Anderson survived a mighty scare from Mikhail Kukushkin.
Jack Sock is the first American to reach the semi-finals of the ATP World Tour Finals event since Andy Roddick in 2007.
By extending his current winning streak to 13 matches, the 36-year-old advanced from the Tour Finals group stage with an unblemished 3-0 record for the 10th time in his glittering career.
Jack Sock, the American number one, came from nowhere to reach the ATP World Tour Finals, reaching London by winning the Paris Masters.
Rafael Nadal is chasing a seventh title in a season and a hat-trick of triumphs on the trot, having been crowned US Open and China Open champion in recent weeks.
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.
Former world number one Sharapova, the 2006 US Open winner in her first Grand Slam since serving a 15-month doping ban, downed the 139th-ranked wildcard 7-5, 6-2 and moved into a fourth-round clash with Latvian 16th seed Anastasija Sevastova.
Marin Cilic explained that his tears at 0-3 down in the second set were more a result of his disappointment at not being able to perform at his best rather than a legacy of the pain.
Roger Federer won his eighth Wimbledon crown without dropping a set.
Roger Federer's eighth Wimbledon victory earned him his 19th overall Grand Slam as wishes poured in.
Federer not only surpassed all other male Wimbledon champions with his eight titles but became the oldest Wimbledon champion in the Open Era.
Roger Federer claimed his 19th Grand Slam with a 6-3, 6-1, 6-4 win over Croatia's Marin Cilic.
Wimbledon 2017 Men's Final Highlights: Roger Federer won a record eighth Wimbledon title and his 19th Grand Slam title with a 6-3, 6-1, 6-4 win over Marin Cilic.
Roger Federer is seeking his record eighth title at the All-England club and has beaten Marin Cilic six times out of seven, but the last two meetings have been complicated.
Cilic won 83 percent of first serve points, while Querrey took 85 percent in the first set.
Wimbledon 2017 highlights: Seventh seed Marin Cilic will play 18-time Grand Slam champion Roger Federer in the men's singles final at Wimbledon after the Swiss beat Tomas Berdych in straight sets on Friday. Cilic quelled Sam Querrey's challenge in four sets to reach his first Wimbledon final.
Scot world No 1 brushed aside Karen Khachanov's challenge while 2015 Roland Garros champion from Switzerland defeated Gael Monfils to reach the last-eight stage.