Kansas City (9-3-2), unbeaten in four games, missed out on a chance to take the lead from D.C. United in the Eastern Conference.
Peterson scored for Kansas City in the 8th minute, but Ianni took a crossing pass from Mauro Rosales and beat Jimmy Nielsen with a shot into the left corner to tie it in the 15th minute.
Seattle (7-4-4) is winless in its last five games.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys