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.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.