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.