Reed hit a 3 with 1:56 remaining to break a 57-57 tie and then made another with 1:03 to play, giving American (9-7, 5-0 Patriot League) a 63-57 lead.
Lehigh (8-10, 1-4) cut the deficit to 63-60 with 33 seconds left and got the ball back after a missed free throw by American. But the Mountain Hawks then missed a layup and Tony Wroblicky hit two free throws for American to extend its lead.
Reed finished with 15 points and Wroblicky added 14. Schoof was 5 of 10 from beyond the arc.
American's 5-0 start in Patriot League play is its best in program history.
Mackey McKnight had 23 points for Lehigh, which has followed up a five-game winning streak by losing five of its past six.
NBA fans will be looking forward to their newest players making plays like this next season.
Tim Legler and Brad Daugherty analyze Ben Simmons and Brandon Ingram, the top two picks in the NBA draft, and agree that Simmons will have a more immediate impact.
Dickie V likes the idea of Oklahoma star Buddy Hield teaming up with Anthony Davis in New Orleans. What did he think of other teams' selections?