Djokovic, the ninth seed, was originally scheduled to play Australian Open semi-finalist Chung Hyeon but the 22-year-old South Korean withdrew with a back injury about an hour before the match was due to start.
Murray was made to fight for two hours and 52 minute
The final will pit power against power when Andreescu takes on her childhood hero Williams, who claimed her first US Open title in 1999 before Andreescu was even born.
'This has been an emotional week and I want to thank everyone for the outpouring of support.'
Konta, Sharapova fall at Rogers Cup in Toronto
Australian Nick Kyrgios blasted 15 aces to blow past Japan's Yoshihito Nishioka 6-2, 7-5 on Thursday and reach the quarter-finals at the Citi Open in Washington.
Next up for the 35-year-old will be another American in 39th-ranked Tommy Paul with a potential semi-final clash against top-seeded Russian Daniil Medvedev, who he defeated in the Australian Open final from a two-sets deficit.
The United States survived a fright from little Latvia on Saturday before winning 3-2 in a Fed Cup qualifier as Serena Williams suffered her first career singles loss in the team event. Switzerland, Spain, Belgium, Slovakia, Germany, Russia and Belarus also moved through to the inaugural 12-nation showdown in Budapest.
Twice Shanghai Masters champion Roger Federer was far from his best against Spain's Roberto Bautista Agut but did enough to reach the quarter-finals with a 6-3, 2-6, 6-4 win on Thursday.
World number one Novak Djokovic blasted past qualifier Alexei Popyrin 6-4, 6-2 to reach the second round of the Japan Open Tennis Championships in Tokyo.
American teenager Amanda Anisimova, fresh off an impressive run at Indian Wells, beat China's Wang Qiang 6-3, 1-6, 6-2 at the Miami Open on Tuesday to set up a second round clash with Spanish third seed Garbine Muguruza.
The 33-year-old left-hander from Luxembourg had lost all five of his previous tour finals but prevailed at the sixth attempt in the Australian Open warm-up event at the Olympic Tennis Centre.
Summary of sports events and persons who made news on Wednesday
IMAGES from the matches played at the Miami Masters on Sunday
Former world number one Andy Murray won his first ATP tour singles match in nearly nine months with a 6-3, 6-7(6), 6-1 victory over American Tennys Sandgren in the opening round of the Zhuhai Championships.
Images from Day 3 of the US Open, at Flushing Meadows, New York.
Williams had little trouble against the 31-year-old German although the gusty breezes at Auckland Tennis Centre played havoc with her ball toss, especially when she was serving for the match at 5-3 in the second set.
Halep through but Stephens exits in Cincinnati
Greek tyro Stefanos Tsitsipas' dream run at the Rogers Cup continued on Friday as the teenager toppled defending champion Alexander Zverev 3-6, 7-6(11), 6-4 to reach the semi-finals in Toronto.
Greek teenager Stefanos Tsitsipas secured the biggest win of his career when he sent Wimbledon champion Novak Djokovic packing in the third round of the Rogers Cup with a stunning 6-3, 6-7(5), 6-3 win on Thursday.
Summary of sports events and persons who made news on Monday
Serena Williams sounded a warning for her fellow Australian Open contenders with a sleek win
The Danish World No 3 ended 2017 with the biggest title of her career in Singapore and returned a day after thrashing Madison Brengle in her season opener to hit 21 winners against eight unforced errors in the 53-minute win over Martic.
A summary of Friday's tennis action from around the world.
World No 55 Haase improved to a 2-2 career record against Zverev, including victories in their last two meetings.
Images from Day 2 of the 2020 US Open in New York
A round-up of tennis matches played on Tuesday.
World number two Simona Halep beat Maria Sharapova 6-2, 6-2 in the China Open third round on Wednesday for her first win over the Russian in eight attempts.
It was Novak Djokovic's first match this year after his Australian Open hopes were dashed when he was deported following an 11-day saga revolving around his decision not to have a COVID-19 vaccination.
World number one Simona Halep swatted aside American Nicole Gibbs while Maria Sharapova was flawless in her straight sets victory over Romania's Mihaela Buzarnescu in the opening round of the Shenzhen Open on Monday.
IMAGES from Day 8 of the French Open at Roland Garros on Sunday.
American qualifier Sachia Vickery completed an astonishing comeback to stun third seed Garbine Muguruza 2-6, 7-5, 6-1 in a second-round win at the BNP Paribas Open in California on Friday.
Under the lights on the stadium court, Williams smashed 39 winners to defeat Azarenka 7-5, 6-3 in a rematch of the 2016 final, which the Belarusian won.
'This was the first time that I played points and that was too much for me today'
Venus Williams and CoCo Vandeweghe won the opening singles matches to give holders the United States a commanding 2-0 lead in their Fed Cup World Group opener against the Netherlands in Asheville, North Carolina on Saturday.
Second seed Sloane Stephens was shocked 2-6, 6-4, 6-2 by Germany's Andrea Petkovic in the second round of the Citi Open on Wednesday, disrupting the American's buildup to her US Open title defence.
Images from Day 6 of the Australian Open in Melbourne on Saturday.
Images from Saturday's action at the Australian Open.
A summary of Thursday's play at the US Open.
The returning Scot also announced his withdrawal from next week's Rogers Cup in Toronto.
