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.
ESPN's Dan Dakich joins The Paul Finebaum Show to discuss the SEC's presence in the NBA Draft.
Ted Kapita was the top-rated recruit from West Virginia in the class of 2015 and recently played at DME Academy in Florida.
With the Suns drafting Tyler Ulis, they now have five guards on their roster who attended Kentucky.