Minutes earlier, the 16-year-old Mu came within 0.13 seconds of Russian Olga Kotlyarova's world best of 1:23.44 over the same distance.
Her time of 1:23.57 was a national record and the fastest in 2019.
The 600m is not recognised in world records because it is run infrequently worldwide.
"I was still hungry," said the 21-year-old Brazier, who two weeks ago set a national record in the indoor 800m. "So I went out a little fast and I was able to hang on."
Mu's triumph was perhaps more stunning given her age and the way she won. The long-striding 2018 Youth Olympic Games silver medallist turned back six-time collegiate champion Raevyn Rogers' challenge and sprinted home.
"I am just blown away," said the teenager. "I don't know what I can do anymore."
Sharika Nelvis came from behind to win the women's 60m hurdles in 7.85 seconds, the year's fastest time, and Olympian Devon Allen claimed the men's race in 7.60 seconds.
The 60m sprints went to Demek Kemp (6.55) and Shania Collins (7.16).
Shelby Houlihan, beaten in the mile on Saturday, added another 2019 best when she won the two mile in 9:31.38.
Olympian Clayton Murphy prevailed in the men's 1,000m in 2:20.36, Katie Nageotte cleared 4.81m to defend her women's pole vault title and Keturah Orji took the triple jump with a best of 14.55m.
With no world indoor championships this year, only a limited number of U.S. elite performers competed in the meeting.
The late scheduling of the outdoor world championships, which will take place in Doha in September, also has affected indoor participation this year with many athletes choosing to train instead.
(Reporting by Gene Cherry in Raleigh, North Carolina; Editing by Ian Ransom)
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