Eaves came off the bench to hit 7 of 13 from the floor and 9 of 12 from the line. Ed Stephens scored 13 points and Gabe McCray added 10. The Bulldogs (6-10) won the rebounding battle 38-28.
Geovonie McKnight paced Miami (6-7) with a career-high 24 points. Eric Washington added 16.
S.C. State led by eight with 1:29 to go. LJ Livingston scored on a dunk, then McKnight tipped one in and Rod Mills made a pair at the line to get within two with 28 seconds left.
After a pair of Ty Soloman free throws for the Bulldogs, Mills scored on another tip-in with three seconds left. Stephens then made a pair at the line to ice it for S.C. State.
Miami led 37-26 at intermission and by as many as 12 early in the second half.