Another good question. A quick review reflects that maybe in just 1 of the 18 "close wins" did Iowa have a big lead and give up a meaningless score to make it closer than it looked - Arkansas State in 2009. The Hawks were ahead 24-7 at the end of the 3rd Quarter and won 24-21. In other words, these games were almost always close. Those 18 wins are:
2000 - Penn State 26-23 (OT)
2002 - Purdue 31-28
2003 - Michigan 30-27
2004 - Penn State 6-4, Purdue 23-21, Minnesota 29-27
2007 - Illinois 10-6
2009 - UNI 17-16, Ark. State 24-21, Michigan 30-28, MSU 15-13
2010 - Missouri 27-24
2011 - Pitt 31-27
2012 - NIU 18-17, MSU 19-16
2013 - Michigan 24-21
2014 - Ball State 17-13, Pitt 24-20
There was also Michigan in '09. I figured there were more than that but it doesn't look like there were.