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.