Fognini finished with 26 winners while between them the pair committed nearly 90 unforced errors. Out of a cumulative total of 25 break points, only nine were converted.
Djokovic reached his 12th Wimbledon quarter-final and is looking for a sixth title at the All England Club, and a record-equaling 20th Grand Slam trophy.
Having won two ATP 250 titles in his career, this was the first tournament win at 500 level for Humbert.
The 23-year-old Russian was made to work for his 6-1, 3-6, 6-3 semi-final victory in just under two hours.
Rublev is the last remaining seed in the Halle draw after Roger Federer and world number two Daniil Medvedev were among the big-name casualties in the early rounds.
After Roger Federer suffered a shock defeat on Wednesday, Zverev, who reached the semi-finals of the French Open last week, also exited in the second round when he lost 7-6 (7/4), 3-6, 6-3 to France's Ugo Humbert.
Two-time Wimbledon champion Petra Kvitova pulled out of the tournament because of an ankle injury. Kvitova said she fell and hurt her ankle during “post-match press requirements” after her first-round victory on Sunday
Having slipped to number three in the world, it was always likely that Nadal, the 13-time champion, would face top-ranked Djokovic before the final.
Federer begins his comeback-proper on Swiss home soil in Geneva on Tuesday, with the 39-year-old legend starting a run of tournaments including the French Open, Halle, Wimbledon and then the Tokyo Olympics.
Nadal, a 13-time French Open winner, is also behind Daniil Medvedev, who suffered a second round exit in Rome to continue his struggles on clay.
Nine-time champion Nadal had to save two match points against Canada's Denis Shapovalov in a 3-6, 6-4, 7-6 (7/3) battle over nearly 3hr 30min.
Nadal's path to a possible sixth Madrid title was cleared of second seeded Daniil Medvedev and fourth-seeded Monte Carlo champion Stefanos Tsitsipas who were both shock third round losers.
US Open champion Thiem, playing his first tournament since Dubai in March, will meet Andrey Rublev or John Isner in the last eight.
Nadal, who captured his first Barcelona title as an 18-year-old at the 2005 tournament, will face Pablo Carreno Busta in Saturday's semi-finals.
The world number three triumphed 6-0, 2-6, 6-2 over 2014 and 2015 champion Nishikori and next faces Britain's Cameron Norrie, a fellow left-hander, for a place in the semi-finals.
Tsitsipas won his last title in February last year at the Open 13 indoor tournament in Marseille — just weeks before France went into lockdown for the first time because of the coronavirus pandemic.
Fourth seed Tsitsipas needed just over an hour to dispatch Britain's Evans, who knocked out world number one Novak Djokovic in the last 16.
Rublev clinched his first win against third-seeded Nadal on his first match point with a typically powerful winner on forehand — a weapon Nadal struggled to contain all match.
Sinner, who reached last year's French Open quarter-finals, defeated Bautista 5-7, 6-4, 6-4 to become only the fourth teen to reach the men's final in the 36-year history of the ATP Miami Masters.
Barty, who is assured of retaining her No 1 ranking next week, will play for the title Saturday against the winner of the second semi-final between No 8 Bianca Andreescu and No 23 Maria Sakkari.