Reed and Jones combined to shoot 17 for 27 from the field and 6 for 11 from beyond the 3-point arc.
Marko Vasic's 3-pointer before halftime gave American (3-15, 1-6) a 35-34 lead it would never surrender.
The Eagles started the second half with a 10-0 run on a 3-pointer from Reed, a Jones' layup, Paris Maragkos' 3-point play and another layup by Vasic in the first three minutes.
Trailing 54-45 with 11:15 left, Lafayette used a 7-2 run to cut the lead to four. But American continued to thwart each Lafayette run as the Leopards never could reduce the deficit to less than four points.