Appling drained a trio of 3-pointers and Denzel Valentine added 12 points for the Spartans (19-2, 8-1 Big Ten), who only held on for the victory when Mike Gessell's layup at the end of extra time bounced off the rim.
Matt Costello helped pick up the slack for injured forwards Branden Dawson and Adreian Payne with a career-high 11 points and 12 rebounds.
Iowa (16-5, 5-3) was paced by Roy Devyn Marble 21 points.
Aaron White ended with 10.
Celebrity Families of 2014 [PHOTOS]