Kent State (1-1) was in control for most of the game and led by 17 with 8:02 to play. But Hampton's Rashad West scored six during a 13-3 run to narrow it to 68-62 with just under two minutes left.
Free throw shooting by McKee and Mike Scott stopped the Pirates' comeback and secured the win.
Vincent Simpson scored 22 points and West had 20 for Hampton (1-2).
Scott scored 14 points, was 10-for-11 from the free throw line and also grabbed six rebounds for Kent State.
The Golden Flashes were 9-for-20 (45 percent) in 3-point shooting.