The Eagles went on a nine-play, 71-yard drive with Jeremiah Williams catching a 3-yard touchdown to tie it at 7-7 with 2:59 left in the third quarter.
With the score still tied early in the fourth quarter, Eagle linebacker Mitch Hartshorne intercepted a pass and returned it 26 yards to the Hightower 37.
On the first play after that, Carter connected with wide receiver Marcus Thomas who was all alone down the left sideline, to take a 14-7 lead with 9:05 to play.
On the next Allen possession, Carter connected with Justin Robinson for a 9-yard touchdown to make it 21-7 with 5:17 to play.
Hightower got a 77-yard return from Darius Johnson on the ensuing kickoff to set the Hurricane up on the Allen 11.
A.J. Highsmith, the son of former Houston Oiler Alonzo Highsmith who is headed to the University of Miami, found Bryce Edwards for the last 11 to make it 21-14 with 5:00 to play.
Hightower, which only opened in 1998, took a 7-0 lead on a 42-yard end-around by Darius Johnson late in the first quarter.
The Hurricanes went to Johnson almost exclusively on third downs in the first half and he converted the first three with receptions of 39, 22 and 23 yards. At the half, Johnson , who has committed to SMU, had five catches for 96 yards.
Carter kept the Eagles in it by completing 10-of-14 for 104 yards the first half. But he was intercepted in the end zone to kill one drive.
