Ohio State center Terence Dials tied a career high with 29 points and added nine rebounds.
The Buckeyes (18-11, 7-8) shot the ball well all night and led the majority of the game, so the loss was especially frustrating for head coach Thad Matta.
"Yeah, this is a tough one," Matta told WBNS radio. "We couldn't defend. They went on a late surge and… You can't go on the road and shoot 54 percent and lose when you've got 19 assists, 11 turnovers, unless you're not defending.
"I'd like to give Iowa credit. They made some shots. Horner's shot there at the end was a tough shot. But, we had no answers. We had nothing. We tried zone, we tried everything. We were matched up, we were switching, everything."
Iowa took its largest lead of the game, 66-60, at the 4:52 mark on a Horner jumper.
However, OSU's J.J. Sullinger responded with a three-pointer, cutting the lead to 66-63 with 4:20 remaining.
A Dials putback made it 66-65 Iowa at the 3:42 mark.
With the defensive intensity heating up for both sides, OSU's Matt Sylvester eventually drew a shooting foul at the 1:55 mark. He made one of two shots and the game was deadlocked at 66-66.
Adam Haluska responded with a three, giving Iowa a 69-66 lead with 1:26 left in the game.
Sylvester matched him with a triple at the 1:05 mark, bringing the teams even again at 69-69.
Iowa's Doug Thomas then converted a three-point play, giving the Hawkeyes (18-10, 6-9) a somewhat comfortable 72-69 advantage with 42 seconds left.
But Dials matched Thomas' effort, putting three points on the board the old fashioned way with a dropstep on the low block and ensuing free throw. With 27.2 seconds left, this back and forth struggle was again tied, 72-72.
But this was Horner's night. He created some space between him and Je'Kel Foster, rose up over Foster, and connected for the eventual game-winner.
The Buckeyes had a chance to win or tie with 3.4 second showing on the clock, but had to go the length of the court to do it. Jamar Butler caught an inbounds pass on the run, but his foot touched the sideline just before reaching midcourt with one second left.
"I guess we stepped out," Matta said. "I didn't see if there was any contact or not. That's inexcusable."
The loss spoiled the latest stellar performance from Dials. The 6-9 junior was nearly unstoppable when he got his hands on the ball, and he played the entire game.
"I thought Terence was really good down low," Matta said. "I thought he gave us everything he had for 40 minutes.
"Offensively, I think we played about as well as could. I'll take 19 and 11, and 54 percent anytime. We just didn't have the ability to get the stops early. I wish I could say it was one guy. It was everybody. They had two guys that killed us: Horner and Haluska. We did a great job on (Greg) Brunner."
Haluska had 22 points. Brunner finished with four. Horner nearly missed a triple-double for the Hawkeyes, with eight rebounds and eight assists (and no turnovers).
For Ohio State, sophomore forward Ivan Harris had 13 points and seven rebounds.
Ohio State began the game on a 7-0 run, including five points from the 6-8 Harris.
The Buckeyes led nearly throughout the first half, taking their largest lead of the game at 15-6 on a Dials dunk at the 14:15 mark.
Iowa took its only lead of the first half, 22-20, on a basket from Carlton Reed at the 8:52 mark.
A Dials basket gave OSU a 35-31 lead late in the half.
But Iowa's Jack Brownlee made a three-pointer at the buzzer, making the count 35-34 OSU at the halftime break.
In the second half, Ohio State was called for a whopping six fouls in the first four minutes. Iowa was in the bonus at the 14:11 mark, when it took its first lead of the second half, 45-43, on a pair of free throws from Mike Henderson.
"The fouls killed us there early in the second half," Matta said.
Ohio State was hoping to reach 20 wins in Matta's first season at the helm. But if the Buckeyes want to have a good chance at doing it, they will now have to pull a major upset their next time on the court.
The nation's undisputed No. 1 team, Illinois (28-0), comes to Columbus at high noon on Sunday for a sold out showdown at the Schottenstein Center. Matta's Xavier team knocked St. Joseph's from the unbeaten ranks late last year. Can he do it again?