Kellogg added seven rebounds and four assists for fifth-seeded Ohio (23-10), which will take on Akron in the quarterfinals on Thursday. Javarez Willis and Maurice Ndour added 13 and 12 points, respectively.
For eighth-seeded Miami (13-18), Willie Moore tallied a double-double with 16 points and 10 rebounds, while Jaryd Eustace came off the bench to score 15.
Ohio shot a lowly 26.9 percent from the field in the first half, but it held Miami to an even worse 23.3 percent. The Bobcats helped make up for their poor field goal shooting with a 10-of-13 showing at the foul line and took a 27-23 lead into the break.
The Bobcats improved their field goal efficiency to 50 percent in the second stanza. After the RedHawks took a two-point lead with under eight minutes to play, Ohio surged ahead for good with six unanswered points and pulled away late by ending the game with a 7-0 spurt.
Both teams had 37 rebounds and 10 turnovers. Ohio earned a 24-15 scoring advantage from beyond the arc.