The 25th-seeded Italian's bid to join compatriot and world number one Jannik Sinner as a major champion this year faces a massive hurdle, however, as he faces seven-times All England Club champion Novak Djokovic in the last four.
After holding in a tight first game, Fritz seized the early break for a 3-1 lead when Musetti netted a backhand, before the American consolidated the advantage in the next with a powerful forehand winner to set the tone for the first set.
The Eastbourne champion continued to crank up his forehand and serve in glorious sunshine, occasionally drawing gasps from Court One fans with rockets from the baseline, and grabbed the lead in the match with an ace.
After the pair exchanged breaks at the start of the second set, Queen's Club runner-up Musetti pounced again to go 5-3 up, and although Fritz erased the deficit the Italian raised his level to edge the tiebreak.
Musetti mixed up his game with chips and slices and forced Fritz into uncharacteristic errors, easing through the third set on the back of two breaks, but he handed the American a way back into the match after dropping the next set.
As shadows covered the manicured turf to make life tough for the players, Musetti built a 5-0 lead in the decider and finished it off on serve when Fritz hit a shot long after falling awkwardly at the net in the previous point.
Musetti's reward is a meeting with 24-time Grand Slam champion Djokovic, who went through to a record-equalling 13th semi-final at Wimbledon after Australian ninth seed Alex De Minaur pulled out of their match with a hip injury.
