Harper, a junior who became the starting quarterback when Noah Johnson was injured earlier in the season, completed passes to five receivers, four of whom scored touchdowns. Anthony had one touchdown, Chris Blair two and LeCharles Pringle two.
Harper improved to 4-0 as the starter this season and has passed for 1,146 yards with 16 touchdowns and no interceptions since Johnson was injured.
Savannah State (3-3) trailed 21-3 in the second quarter before closing the gap to 21-17 in the second quarter. First, the Tigers scored on a 15-yard pass from D'Vonn Gibbons to Cameron White. Then on Alcorn State's next play Harper was sacked and his fumble was recovered by Cam Brown in the end zone.
Harper hit Blair for a 24-yard score and Alcorn State (5-2) led 28-17 at halftime. In the third quarter, Harper and Anthony connected for 84 yards and Trey Turner had a 3-yard TD run to cap the homecoming win.