The teams traded goals 2 minutes apart early in the contest and it appeared they would finish in a draw.
Pappa, however, took a feed from Federico Puppo in the 93rd minute and drove a shot from outside the box into the left corner of the net.
Juan Pablo Angel gave Chivas the lead in the 23rd minute, but Austin Berry soon tied it for Chicago.
The three points lifted Chicago (3-2-2) into third place in the Eastern Conference.
Chivas (3-6-0) has lost three in a row.