The top-seeded Italian made light of the day's play being delayed by four hours due to torrential rain and exposed the gap between him and the British number one once he came through a tough first set.
The World No 9 Berrettini broke Murray twice in the first set and took an early break in the second for a 3-0 lead. He never looked back, mixing powerful groundstrokes with some deft touches at the net.
The Italian teenager will face the 20-time Grand Slam winner for the second time, having impressed against Nadal in last year's French Open quarter-finals despite losing in straight sets.
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.
Monte Carlo Masters: Stefanos Tsitsipas beats Dan Evans in straight sets to set up final against Andrey Rublev
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.
World number one Djokovic was broken five times by the Briton in their last-16 clash and suffered his first loss of the year, having won the Australian Open for the ninth time in February.
What matters far more in the scheme of things than the result or the way it came about is that Federer cares about success and can conjure up what's necessary to find it.
"It's been a long and tough road for me," said Federer, who hasn't played a match since a semis defeat to Novak Djokovic at the Australian Open in January 2020, 405 days ago.
Humbert, who is on a seven-match winning streak after winning the Antwerp title last month, missed four match points but battled to a 7-6 (7/4), 6-7 (6/8), 7-6 (7/3) victory.
World number one Novak Djokovic should put his hand up and accept responsibility after Grigor Dimitrov and Borna Coric tested positive for COVID-19 while participating in his Adria Tour exhibition tournament, Briton Dan Evans said.
Novak Djokovic is fretting about harsh restrictions on players’ entourages and other extreme changes proposed for the US Open — and saying he might not participate if it is played.
Britain’s Dan Evans dismisses Novak Djokovic's US Open concerns over COVID-19 protocols, says compromises should be made
Dan Evans believes Novak Djokovic’s concerns about players having only one member of their support staff at the US Open does not apply to the majority of the field and compromises should be made when action resumes.
Briton Dan Evans says a sports psychologist described him as one of the angriest people he had ever met during his one-year ban from tennis for cocaine use in 2017.
Dubai Tennis Championships: Novak Djokovic bolts into semi-finals; Stefanos Tsitsipas comes from set down to beat Jan-Lennard Struff
In all, Djokovic sent down 19 winners to Khachanov’s nine, won 89% of his first serve points, nine of 11 forays to the net, and wrapped up the one-sided affair in just 66 minutes.
Rotterdam Open 2020: Defending champion Gael Monfils beats Dan Evans in straight sets to advance to semi-finals
Monfils will meet Serb Filip Krajinovic or Russian seventh seed Andrey Rublev, while Spain’s Pablo Carreno Busta faces Canadian teenager Felix Auger-Aliassime in the other semi-final
Rotterdam Open 2020: Unseeded Slovenian Aljaz Bedene upsets World No 6 Stefanos Tsitsipas in straight sets to book quarter-final spot
Russian Andrey Rublev continued his impressive form with a 7-5, 6-3 victory over Alexander Bublik to extend his win record in 2020 to 13-1
ATP Cup 2020: Britain in pole position to qualify for knockouts, could top Group C and face Australia in quarter-final
A 6-2, 6-3 doubles victory for Jamie Murray and Joe Salisbury over Albot and Cozbinov completed the 3-0 win over Moldova, leaving Britain in a good position to qualify for the quarterfinals
The 32-year-old Murray, who returned from hip surgery in June, made heavy weather of beating 79th-ranked Dutchman Tallon Griekspoor on Wednesday in Britain’s opening group match.
Davis Cup Finals 2019: Rafael Nadal rescues Spain to progress to semi-finals, heartbreak for Novak Djokovic's Serbia
Novak Djokovic played singles and doubles matches on Friday but couldn’t keep Serbia from losing to Russia 2-1 in the quarter-finals of the Davis Cup.