Chievous has nine double-doubles in points and rebounds in his last 19 games.
Hampton darted to a 7-0 lead, and Savannah State didn't score until Chris Martin hit a 3 with 16:21 to play before halftime. The Tigers rallied to tie it at 28 at the break.
The Pirates started the second half with an 18-6 run in which Chievous scored eight points. Brian Darden's layup with 13:01 left gave Hampton (11-7, 7-0 Mid-Eastern Athletic) a 46-34 lead.
Chievous and Reginald Johnson Jr. then scored 13 of the Pirates' next 16 points as Hampton took a 62-45 lead with 6:05 remaining.
Martin scored 15 points for Savannah State (7-10, 3-3) while Lenjo Kilo had 11 points and 10 rebounds.