In the first game of the afternoon, Italian Musetti edged a three-set encounter 3-6, 6-3, 3-6 against Jordan Thompson to be the first to book his place in Sunday's final.
Having won the opening set, Thompson fought back to take the game to a decider. Despite saving five break points in the eighth game, the Australian was eventually beaten as Musetti booked his place in his first grass final.
Later that afternoon, Paul came through an all-American contest in straight sets, emerging a 6-4, 7-6 (7-1) victor over Sebastian Korda to set up a maiden encounter with the Italian.
27-year-old Paul quickly found a break in the second game against his opponent and despite Korda replying with a break of his own in the seventh game, was unable to recover from his slow start.
The second set flowed with both players trading break points, but an error-strewn display from Korda allowed Paul to see out the contest with relative ease to become the first American finalist at Queen's since 2010
Data Debrief: Musetti faces
Musetti maintained his unbeaten record against his Australian opponent, having won their previous encounter in straight sets in Adelaide back in January. The Italian also won 45 of his 62 first-serve points, a success rate of 73%.
After three consecutive defeats against Korda, Paul has now won two of his last three meetings with his compatriot. However, his opponent bettered him on first-serve points, winning 74% compared to Paul's 62%.
It took the American just 88 minutes to get his 6-1 7-6 (10-8) win after a front-footed, aggressive approach.
Paul cruised through the opening set but looked like he might be forced into a decider after failing to serve out the match at 5-4.
The Italian edged them into a tie-break, but Paul rallied from 1-4 down to get his hands on the title.
His 27th tour-level win of the season also ensured he will surpass Taylor Fritz to become the American number one for the first time in his career on Monday.
Data Debrief: Paul hits cruise control
It was a dominant performance from Paul throughout Queen's as he only dropped a single set on his way to capturing his third ATP Tour title.
On Sunday, he made just six unforced errors as he came out on top in his first-ever meeting with Musetti.
The world number nine beat British hope Cameron Norrie 6-4 6-7 (5-7) 6-3 in the London showpiece match on Sunday, setting himself up ideally ahead of a Wimbledon mission later this month.
Whereas Becker was 17 when he triumphed at Queen's Club in 1985, going on to be champion at Wimbledon just weeks later, Berrettini is 25 years old and established as a leading player.
His big serve – an aspect of his game he shares with vintage Becker – proved a huge asset against Norrie as Berrettini served 19 aces and won 91 per cent of points when landing his first delivery.
Norrie could not forge a break point but did commendably well to force a deciding set in a match that lasted three minutes short of two hours.
Berrettini said he had experienced an "unbelievable week", lifting his first title at ATP 500 level, and he was blown away by the Becker link.
"If I think about his name and my name, it's crazy," he said in an on-court interview.
"I was dreaming about playing this tournament. I was watching when I was a kid and now I had the chance to lift the trophy. It's a dream come true."
Berrettini could be a threat to anyone if his serve fires at Wimbledon, and he was proud of how he fended off Norrie.
"I didn't check the numbers during the match. I knew I was serving well," said Berrettini. "I knew it was important because in the rallies this guy is dangerous. I knew I had to play my best tennis."
Berrettini said his celebrations were likely to be muted, given he is in a pre-Wimbledon bubble, predicting his team would limit his post-match treats to "probably room service and sparkling water".
There would be cause for greater cheer if Berrettini goes on a run at the All England Club, with Wimbledon due to begin on June 28. His previous best performance at Wimbledon was a run to the fourth round two years ago.
Berrettini told Amazon Prime: "I know it's going to be a really tough tournament.
"Probably all the players have extra motivation to play well there so it's going to be tough, but I have a lot of confidence."
Andrey Rublev was a surprise first-round loser at the Halle Open, while numerous seeds fell on the first day of the Queen's Club Championships.
Rublev came unstuck against Georgian Nikoloz Basilashvili, succumbing to a 7-6 (7-1) 6-4 loss as the world number eight crashed out in Germany.
Laslo Djere progressed after Henri Squire retired when 4-3 down, while sixth seed Pablo Carreno Busta secured a 6-3 7-6 (7-5) over French Open quarter-finalist Holger Rune.
Ugo Humber got the better of a topsy-turvy affair against qualifier Radu Albot, eventually triumphing 6-7 (4-7) 7-6 (7-4) 7-5 and Mackenzie McDonald defeated Marc-Andrea Huesler in straight sets.
Fourth favourite Taylor Fritz went down 6-3 6-3 against British wildcard Jack Draper, his first career win against a top-20 ranked player.
Reilly Opelka, the eighth seed, crashed out in the first round to New Zealand's Alex de Minaur, who claimed a straightforward 6-4 6-4 win.
Grigor Dimitrov, who won the event in 2014, battled past third seed Cameron Norrie 6-7 (2-7) 6-1 6-4, while Spaniard Alejandro Davidovich Fokina eased past compatriot Albert Ramos-Vinolas 7-5 6-4.
Alexander Bublik was 6-3 up before Italian Lorenzo Musetti retired, while seventh seed Marin Cilic capped the day's play in London by beating home hope Liam Broady 6-1 4-6 7-5.
The French Open runner-up struggled to get going as he fell to a 7-6 (7-4) 7-6 (7-2) defeat to the world number 180, who was backed by a boisterous home crowd throughout.
Ruud struggled from the off as Peniston forced four break points in the Norwegian's first service game, and his miserable outing was rounded off when his opponent raced into a 5-1 lead before serving out a second-set tie-break.
After claiming the scalp of the world number five, Peniston told the BBC: "I can't really believe it. It feels like a dream. It doesn't feel real.
"I think I've been playing well. Casper is an unreal player and he did so well at the French Open, so I knew it was a tough ask. Four or five years ago I was sitting in the crowd just watching so to be here now is just unreal."
Ruud was not the only big name to fall at the first hurdle, with fifth seed Diego Schwartzman going down 6-1 6-4 against big-serving Sam Querrey to become the fourth of the top five seeds to fail to reach the round of 16.
Second seed and defending champion Matteo Berrettini is the exception after faring much better against another home favourite, cruising past Dan Evans 6-3 6-3, while Stan Wawrinka downed Francis Tiafoe 7-6 (7-2) 6-7 (6-8) 7-6 (7-5), and Denis Shapovalov's clash with Tommy Paul was suspended by darkness at one set apiece.
Elsewhere, world number six Stefanos Tsitsipas progressed through his opening match at the Halle Open, beating Benjamin Bonzi 7-6 (7-1) 1-6 6-3 to set up an enticing last-16 clash with Nick Kyrgios, who bested Daniel Altmaier 6-3 7-5.
Fourth seed Felix Auger-Aliassime also progressed after being taken to three sets, beating Marcos Giron 6-3 5-7 6-3.
Meanwhile, defending champion Ugo Humbert will face a tough round-of-16 match against fifth seed Hubert Hurkacz after the Pole overcame Maxime Cressy 6-4 4-6 6-4.
