The Greyhounds (2-4) took off to a 15-3 lead in the first eight minutes and led throughout.
Loyola led 33-23 at halftime. Jermaine Marrow's fastbreak bucket for the Pirates closed the gap to 55-53 with just under seven minutes to go, but he was called for a technical for celebrating and Kostecka made both free throws.
Loyola made five free throws in the final 1:02 to seal the win.
Marrow led Hampton (1-4) with 22 points. Kalin Fisher scored 13 and Ben Stanley had 11.