Sunderland dominated the early stages but Marcus Hahnemann saved brilliantly from Marcus Stewart and Julio Arca.
The Black Cats took the lead when Arca nodded in Stewart's right-wing centre.
Reading hit back and Kitson prodded the ball home 15 minutes from time before Jeff Whitley fouled Steve Sidwell in the box and Kitson netted the penalty.
Reading manager Steve Coppell:
"Before the game I felt we had nothing to lose.
"This is the first time I have been to the Stadium of Light and it can be an
intimidating place.
"But we got the bit between our teeth in the end and looked the part instead of being lambs to the slaughter."
Sunderland: Myhre (Ingham 45), Wright, Caldwell, Breen, McCartney, Lawrence (Whitley 70), Whitehead, Robinson, Arca, Stewart, Brown (Deane 77). Subs Not Used: Elliott, Danny Collins.
Booked: Brown, Wright, Robinson.
Goals: Arca 52.
Reading: Hahnemann, Murty, Ingimarsson (Keown 56), Sonko, Shorey, Harper, Sidwell, Newman (Ferdinand 66), Brooker, Kitson, Forster. Subs Not Used: Hughes, Morgan, Young.
Booked: Sidwell.
Goals: Kitson 76, 82 pen.
Att: 34,237
Ref: L Mason (Lancashire).