She clocked 53.13 seconds to win by a margin of 0.42s.
"The reality of winning is even better than the dream. Olympic champion in front of my name," said Muhammad, runner-up at the 2013 world championship.
The 26-year-old had come to the Rio Games as the fastest woman in the event this year.
Dalilah Muhammad (USA) of USA clears a hurdle
Image credit: Reuters
Petersen, the European champion, ran 53.55 seconds, and Spencer recorded a personal best of 53.72.
The result underlined US supremacy in the hurdle events, with Kerron Clement winning the men's 400m earlier on Thursday and Brianna Rollins, Nia Ali and Kristi Castlin completing an American podium sweep in the 100m on Wednesday.