Goffin, who won the event in 2014, fell to a 6-3 6-3 defeat to three-time champion Gilles Simon, who is set to retire at the end of the 2022 campaign.
Simon needed 93 minutes to wrap up his victory over the four-time grand slam quarter-finalist, teeing up a round-of-16 meeting with Italy's Lorenzo Sonego.
"We've known each other for a very long time and I’m always happy to play against [Goffin] one more time before the end," Simon said after the win.
"It was really perfect from the start until the end and that's how I won this one."
Elsewhere, Basilashvili was a set down in his meeting with Bergs when the Belgian qualifier was forced to retire through injury, allowing the fifth seed to progress to a meeting with Arthur Rinderknech.
Rinderknech downed Spain's Jaume Munar in three sets to reach the next round, while Emil Ruusuvuori comfortably saw off Jiri Lehecka 6-4 6-4.
Top seed Hurkacz defeated German qualifier Peter Gojowczyk 6-4 7-6 (7-4) to stand on the brink of a third title of the year.
The world number 13 from Poland won 79 per cent of the points on his first serve and sealed victory in an hour and 37 minutes.
Gojowczyk saved five break points but was unable to pull off an upset in Metz.
Hurkacz said: "Peter played a really great match. He was super tough to play against, so I am proud of myself that I managed my emotions and played a good tie-breaker.
"I was trying to keep holding serve to stay in the second set and ended up taking the set in the tie-breaker."
Carreno Busta ended Gael Monfils' bid to win the title on home soil, the Spaniard triumphing 7-5 7-6 (10-8).
Monfils was 5-3 up in a second-set tie-break but failed to force a decider as Carreno Busta advanced for a showdown with Hurkacz.
James Duckworth is into his first ATP Tour final after beating eighth seed Ilya Ivashka 6-3 7-6 (7-4) at the Astana Open.
The Australian will face Kwon Soon-woo, who upset second seed Alexander Bublik 3-6 7-5 6-3.
The Pole did not drop a set on his way to the final and produced yet another impressive outing to down Carreno Busta 7-6 (7-2) 6-3 in just 82 minutes.
Carreno Busta did, however, take an early lead and have Hurkacz reeling from a break down in the first set but the 24-year-old, who defeated former world number one Andy Murray this week, responded efficiently.
Having come from 3-1 down to 4-4, Hurkacz did not look back as his sharp first serve caused Carreno Busta all sorts of problems, most notably to secure the first-set tiebreaker with ease.
The pair continued to exchange breaks at the beginning of the second set but Hurkacz played well from the baseline and held serve to clinch his first trophy outside of the United States.
His victory means he holds a 4-0 record in ATP Tour finals and also saw him inflict revenge on Carreno Busta, who won the previous head-to-head clash in Cincinnati last month.
Hurkacz will be looking for doubles glory on Sunday as well, as he teams with international compatriot Jan Zielinski.
Top seed Hurkacz beat Daniil Medvedev and Roger Federer on the way to the semi-finals at Wimbledon, and previously beat Murray in Cincinnati.
Hurkacz is ranked 13th in the world and is pushing for a place at the ATP Tour Finals, and he edged closer to a fourth career title by defeating Murray again in Metz.
The 24-year-old prevailed 7-6 (7-4) 6-3 over the former world number one, who was playing in his first ATP Tour quarter-final of the year.
"Andy is an unbelievable competitor, he has achieved so much throughout his career," Hurkacz said. "He is coming back from a tough injury and playing at a very high level, so he is amazing and you can be inspired by his results."
Next up for Hurkacz is Peter Gojowczyk, who overcame Marcos Giron 3-6 6-1 6-3 and is backing up his recent US Open run in strong fashion.
The other last-four match will take place between French home favourite and third seed Gael Monfils, who has reached his first tour semi-final since February last year, and Pablo Carreno Busta.
Carreno Busta, the Spanish second seed, needed three sets to beat Holger Rune, while Monfils had an easier time of it against Nikoloz Basilashvili, winning 6-3 6-3.
At the Astana Open, second seed Alexander Bublik beat Carlos Taberner 6-3 6-4, as he hunts a first singles title.
A crowd favourite in Kazakhstan, whom he has represented since 2016, Russian-born Bublik faces a semi-final against Soonwoo Kwon, who got past Laslo Djere.
Fifth seed John Millman succumbed to fellow Australian James Duckworth, who will face Ilya Ivashka for a place in the final.
Korda was playing his first indoor match since the decider of the Next Gen ATP Finals last November, and Hugo Gaston represented a tough opening test.
But the American prevailed in straight sets against the home favourite, winning 6-3 7-6 (7-2) after defending set points in the second set and blowing his opponent away in the subsequent tie-break.
Another tricky opponent awaits, with number three seed Lorenzo Musetti up next in the second round.
Musetti's Italian compatriot Sonego also succeeded in Monday's only other main-draw match, beating sixth seed Aslan Karatsev 7-5 6-3 to set up a last-16 clash with either Gilles Simon or David Goffin.
In the qualifying section, three-time grand slam champion Wawrinka beat Zsombor Piros 6-7 (4-7) 6-2 6-0 to reach the first round, where Joao Sousa awaits.
The winner of that match will face top seed Daniil Medvedev in the last 16.
World number four Medvedev fell to a 6-4 6-7 (7-9) 6-3 loss against three-time major winner Wawrinka, who will next meet Mikael Ymer after his straight-sets win over home favourite Gregoire Barrere.
Second seed Hurkacz did not experience such struggles against Thiem as the Pole cruised to a 6-3 6-4 as he served 12 aces in a dominant performance in Metz.
Hurkacz will face Arthur Rinderknech in the next round after the Frenchman battled to a 7-6 (13-11) 6-3 triumph over fifth seed Nikoloz Basilashvili.
Alexander Bublik, the seventh favourite in France, was also made to work for his progress to the quarter-finals, downing Emil Ruusuvuori 6-7 (4-7) 6-4 6-3.
Fourth seed Holger Rune awaits Bublik after Benjamin Bonzi retired due to injury when 6-4 4-1 down against the Dane.
Lorenzo Sonego coasted through his second-round clash to defeat Gilles Simon 7-6 (7-2) 6-4 to tee up a last-eight clash with Sebastian Korda.
Murray followed up Tuesday's triumph against Ugo Humbert with a straight-sets victory over the Canadian, reaching the quarter-finals with a 6-3 6-3 success.
The last eight will see Murray face either Lucas Pouille or top seed Hubert Hurkacz, who he lost to in Cincinnati last month.
However, Murray has since played an exceptional five-setter with Stefanos Tsitsipas at the US Open and the former world number one and three-time grand slam champion is feeling increasingly positive about his game.
"This period has been the most tournaments I've played [recently] and my body feels good and I'm starting to gain just a little bit of confidence with each match," Murray said in his on-court interview.
"[I'm] starting to see the points and how I want to play them again, which is great. There have been times in the past year where I've been a little bit confused and not seeing how the points are developing and stuff, which for me was always a strong part of my game and it made me feel quite uncomfortable on the court when I was feeling that way.
"I'm starting to get that back and the results are coming and my tennis is getting better."
The two other last 16 matches saw second seed Pablo Carreno Busta defeat Mikael Ymer 7-5 6-2, while fifth seed Lorenzo Sonego fell victim to a comeback from teenager Holger Rune, who prevailed 6-7 (6-8) 6-4 6-4.
Pouille came from behind to set up his clash with Hurkacz with a three-set win over qualifier Brayden Schnur, and Peter Gojowczyk was victorious in another first-round match.
At the Astana Open, defending champion John Millman came through a marathon match with Jaume Munar to reach the quarter-finals. The Australian took victory 6-4 6-7 (5-7) 7-5 after three hours and nine minutes.
Seventh seed Laslo Djere needed three sets to see off Lorenzo Musetti but eighth seed Ilya Ivashka had little difficulty beating Timofey Skatov in straight sets.
There were also wins for James Duckworth, Kwon Soon-woo, Emil Ruusuvuori and Carlos Taberner.
In Metz, France, unseeded Italian Sonego swept to a 7-6 (7-3) 6-2 victory in the trophy match, collecting the third ATP title of his career.
He enjoyed a stellar week at the ATP 250 event, following up wins over Gilles Simon and Sebastian Korda with a semi-final victory against second seed Hubert Hurkacz, not dropping a set across his four matches.
Sonego, who reached a career-high ranking of 21st in February, had drifted to 65th in the months since, but the ATP said he would climb back into the top 50 as a result of his title run. The ATP's live rankings on Sunday showed him making a leap of 20 places to number 45.
Bublik, the seventh seed, had reached the final after Stan Wawrinka withdrew from their semi-final due to injury. He kept pace with Sonego on Sunday in a tight first set where serves dominated and neither man could force a break, with success for the Italian in the tie-break breaking the resistance of his Kazakh opponent.
The second set proved to be one-sided as Sonego added the title to his previous triumphs on tour, also extending his winning head-to-head record against Bublik to 4-0.
This indoor hardcourt success followed previous wins on grass in Antalya in 2019 and on clay in Cagliari last year.
Sonego said in an on-court interview: "This is a really emotional moment for me. I'm really happy because I played my best tennis this week. It's been a tough year and I want to enjoy this moment."
World number 84 Ruusuvuori saved a set point in the first-set tie-break on his way to a 7-6 (8-6) 6-4 victory and will now face Ilya Ivashka for a place in the semi-finals.
There was nearly another upset as home hopeful Alexander Bublik, seeded second, had to recover from a set down to overcome Miomir Kecmanovic 2-6 6-3 7-5.
Carlos Taberner awaits Bublik in the next round after the Spaniard beat Egor Gerasimov 5-7 7-6(5) 7-5.
Kwon Soon-woo and James Duckworth saw off Dusan Lajovic and Filip Krajinovic respectively in straight sets to remain a course for glory.
At the Moselle Open in Metz, meanwhile, Gael Monfils took out Philipp Kohlschreiber 7-6(2) 6-4 to reach the quarter-finals on home soil.
Tournament favourite Hubert Hurkacz made light work of 2016 champion Lucas Pouille with a 6-2 6-3 victory to set up a meeting with Andy Murray in the quarter-finals.
Elsewhere on Thursday, German qualifier Peter Gojowczyk proved too strong for Karen Khachanov and will now face Marcos Giron, who upset fourth seed Alex de Minaur.
On the same day fellow countryman Roger Federer would hang up his racquet at the Laver Cup, Wawrinka was forced to go all the way by his opponent in Metz, eventually winning 6-4 4-6 7-6 (7-5).
The three-time grand slam champion, whose injury struggles and form have seen him tumble to 284 in the world rankings, served up seven aces to Ymer's two, and made no double faults.
Victory moves him into the last four, where he will meet seventh seed Alexander Bublik after the Kazakh saw off Holger Rune in another three-set encounter with a 6-3 5-7 6-4 win.
Defending champion Hubert Hurkacz is also through to the semi-finals after making quick work of home favourite Arthur Rinderknech, winning 6-3 6-2.
The world number 10 will face Lorenzo Sonego next after the Italian also came through his quarter-final in straight sets against Sebastian Korda.
Wawrinka came through two qualifying matches to take his place in the main draw before defeating Sousa 7-6 (7-1) 6-2 in Metz on Wednesday.
The three-time grand slam champion's victory was only his fourth in a main draw at tour-level this year following a 13-month absence due to a foot injury.
Wawrinka said after setting up a showdown with top seed Medvedev: "It's the first time I won three matches in the same tournament for more than two years, so it's great.
"I'm getting confidence from winning a few matches, so I'm feeling a bit more relaxed, the way I'm moving. I think the level was good from me, and I'm happy with the win."
Dominic Thiem also advanced at the indoor hard-court event, seeing off Richard Gasquet 6-3 7-6 (7-3).
Sebastian Korda was the first man to seal a quarter-final spot, sending third seed Lorenzo Musetti packing with a 6-3 7-6 (8-6) victory in the last match of the day.
Meanwhile, Alexander Bublik, Gregoire Barrere and Benjamin Bonzi were the other first-round winners.
