Damian Harrell had 10 catches for 104 yards and three touchdowns for Chicago (1-1). Dan Alexander caught three TD passes and had a 1-yard scoring run.
Graziani tossed a 14-yard touchdown pass to Jackson with 1:14 left in the third quarter to give Philadelphia a 43-35 lead.
Graziani also had a 6-yard TD run in the fourth quarter for the Soul.