Anderson finished with 17 points, Williams had 16, and Jones added 11 for Robert Morris (8-4), which hit 13 of 27 attempts from 3-point range.
There were seven lead changes and four ties over the first 6 minutes of the first half before Jones broke open a 16-all game with a 3-pointer. The Colonials led by at least two the rest of the half and took a 40-34 lead into intermission.
Louisiana-Lafayette (4-8) rallied to take a 52-47 lead in the second half but Williams, Anderson, and Russell Johnson hit consecutive 3-pointers to put Robert Morris up for good, 56-52, with 8:02 left to play.
Mbamalu Bryant led Louisiana-Lafayette with 21, Elfrid Payton had 19 but the Ragin' Cajuns hit just 8 of 17 free throws.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.