Grzegorz Rasiak headed the Royals into the lead in the 16th minute and it looked as if they were set to pick up what would have been only their second home win out of 11 Championship matches.
The hosts pressed throughout the game and Rasiak and Kebe both had chances to put the game beyond doubt.
And with 15 minutes to go Reading should have sealed all three points. Marek Matejovsky saw his close-range shot parried by Lillis but only as far as Sigurdsson who drilled wide of the left upright.
But struggling Scunthorpe, who have shown signs of improvement of late, snatched a point 10 minutes from time, Hooper slotting home Paul Hayes’ cross from close range.