Nicholas was 3 of 8 from deep while Steele was 4 of 9.
Lafayette (1-6) led 26-24 at halftime but Monmouth opened the second half with an 18-9 run to go up 42-35 and pull away with 12:58 left to play.
Stephen Spinella had six points during the run, Nicholson chipped in four and Steele capped the spurt with back-to-back 3-pointers.
Spinella, Steele, and Nicholson combined for seven of Monmouth's 19 steals while Dion Nesmith led the way with six steals of his own.
Monmouth (3-4) has won three straight games after a 1-4 start.
Tony Johnson led Lafayette with 14 points, nine rebounds, seven assists and five steals. Johnson is shooting 56 percent (34 of 60) from the field this season.
Maryland point guard Melo Trimble has withdrawn from the NBA draft and will return to College Park for his junior season, sources told ESPN.
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.