Marquette found difficult sledding with a 28-24 halftime advantage but began the second half with a 22-12 spurt to forge its biggest lead at 50-36 after Lazar Hayward's layup with 12:06 remaining.
UC drew within 50-46 with 9:31 left after a 13-2 run but eight straight points gave the winners a 64-52 lead with 4:09 left and the contest was history.
Jerel McNeal had 13 points and seven assists for Marquette.
Wesley Matthews had 11 points with nine assists, while Barro added 10 rebounds for the Golden Eagles (16-4, 6-3 Big East), who have won three in a row. Matthews has scored in double figures in five straight games.
Cincinnati was led by Deonta Vaughn's game-high 23 points.
Vaughn was the only player in double digits for the Bearcats (10-12, 5-5), who lost for the third time in their last four games.