The Tigers struggled to put away the Knights and had only a three-point lead when Crawford hit his long-range shot with 5:51 to play.
Memphis allowed just two points over the next 3:30 and pulled away to win its fourth in a row.
Joe Jackson led the Tigers with 17 points, five rebounds and five assists, pushing them to 16-4 for the season and to 6-2 in the American Athletic Conference.
Crawford added 12 points, Geron Johnson had 10 and the Tigers hit 51 percent from the field.
Central Florida, which battled the Tigers to a 39-39 tie in the first half, came up with 24 points and 12 rebounds from Isaiah Sykes. The Knights fell to 9-9 and to 1-6 in the AAC.