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.
With intel from NBA GMs, Chad Ford checks in with the draft tiers rankings. See how all the top prospects shake out in the eyes of NBA teams.
NBA draft prospect Kris Dunn is excited to see Game 7 between the Cavaliers and the Warriors, he breaks down the constant comparison between LeBron James and Steph Curry and looks forward to playing with or against some of these guys next season.
Arizona's success on the court has forced the Wildcats to regularly sign large classes, and 2017 is shaping up to be more of the same.