Muhammed sank 8 of 15 shots, including 5 of 9 from 3-point range, and added six assists for Troy (3-0). Eugene came off the bench to make half of his 12 shots with two 3-pointers, sinking 8 of 9 free throws.
Troy won for just the second time in 11 meetings in a series that began in 1947. That year Florida State beat Troy (State) 57-37 in the second game of the Seminoles' inaugural season.
Florida State, which had never lost the first two games of a season since Leonard Hamilton took the reins in 2002, is now 0-3.
Cam'ron Fletcher sank a jumper to get Florida State within 54-52 with 9:13 left to play. Eugene answered for Troy with a layup and two free throws and Christian Turner dunked to push the Trojans' lead to 60-52.
FSU pulled within three points twice and trailed 68-64 with 2:16 remaining, but Zay Williams buried a 3-pointer, Eugene scored on a layup and Muhammad sank a 3 to cap an 8-0 run that sealed the win for the Trojans.
Williams finished with 12 points and six rebounds. Kieffer Punter scored 10 with nine rebounds. He and Muhammad both had six assists.
Darin Green Jr. buried 7 of 9 from 3-point range and scored 24 to lead FSU. Fletcher finished with 15 points and 10 rebounds. Caleb Mills scored 14 with four assists.
The Seminoles, who posted an 85-9 record at home over the past six seasons, are 0-2 this season.
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