The Spartans trailed for most of the defensive-oriented battle, but moved in front with 9 minutes to play and came through down the stretch to defeat the Hawkeyes for the 10th time in their last 11 meetings.
Appling converted two foul shots with 20 seconds to go to give Michigan State a 60-57 lead.
Iowa's Anthony Clemmons then made the first of two free throws and missed the second, but he grabbed his own rebound and was fouled by Appling. Once again Clemmons could make just 1-of-2 from the line, after which Appling hit two more with 9 seconds left to account for the final score.
Clemmons failed to hit a 3-point attempt at the buzzer.
Michigan State advanced to 13-3 for the season and to 2-1 in the Big Ten Conference race. Iowa is 11-5 and 0-3.
The Hawkeyes had to endure a brutal start to their Big Ten season, having opened with games against Michigan and Indiana -- both ranked among the top five teams in the nation.
Branden Dawson led Michigan State in scoring with 17 points, Gary Harris had 14 and Appling contributed 12. The Spartans shot just 40 percent from the field, but they came up with 12 steals and forced 18 turnovers overall.
Zach McBabe scored 15 points off the bench to pace Iowa.